Yay! Managed to get a backtrace.

Please note that the symptoms are linked to my connection being particularly crappy (mobile phone tethering) and sockets timing out. I event got a "too many imap connections for this account" error message.

After I understood that Thunderbird was not closing properly, I attached gdb to it, killed Thunderbird, and ran a backtrace. Here comes the full backtrace.

0x00007f7ea666f0bd in read () from /lib/libpthread.so.0
(gdb) bt
#0  0x00007f7ea666f0bd in read () from /lib/libpthread.so.0
#1  0x00007f7ea538cbba in nsAppShell::EventProcessorCallback (
    source=<value optimized out>, condition=<value optimized out>, 
    data=0x7f7e9b3d1fd0)
    at /home/jonathan/Code/comm-central/mozilla/widget/src/gtk2/nsAppShell.cpp:66
#2  0x00007f7ea10b86f2 in g_main_context_dispatch () from /lib/libglib-2.0.so.0
#3  0x00007f7ea10bc568 in ?? () from /lib/libglib-2.0.so.0
#4  0x00007f7ea10bc71c in g_main_context_iteration ()
   from /lib/libglib-2.0.so.0
#5  0x00007f7ea53a23c7 in nsBaseAppShell::DoProcessNextNativeEvent (this=0xf, 
    mayWait=-1871547345)
    at /home/jonathan/Code/comm-central/mozilla/widget/src/xpwidgets/nsBaseAppShell.cpp:161
#6  0x00007f7ea53a25b1 in nsBaseAppShell::OnProcessNextEvent (
    this=0x7f7e9b3d1fd0, thr=0x7f7e9b3364c0, mayWait=1, 
    recursionDepth=<value optimized out>)
    at /home/jonathan/Code/comm-central/mozilla/widget/src/xpwidgets/nsBaseAppShell.cpp:299
#7  0x00007f7ea569fd11 in nsThread::ProcessNextEvent (this=0x7f7e9b3364c0, 
    mayWait=1, result=0x7fff9072766c)
    at /home/jonathan/Code/comm-central/mozilla/xpcom/threads/nsThread.cpp:517
#8  0x00007f7ea566fcd1 in NS_ProcessNextEvent_P (thread=0xf, 
---Type <return> to continue, or q <return> to quit---
    mayWait=-1871547345) at nsThreadUtils.cpp:250
#9  0x00007f7ea4b5d8e6 in nsSyncStreamListener::WaitForData (
    this=0x7f7e80e7d250)
    at /home/jonathan/Code/comm-central/mozilla/netwerk/base/src/nsSyncStreamListener.cpp:58
#10 0x00007f7ea4b5d93a in nsSyncStreamListener::Available (
    this=0x7f7e80e7d250, result=0x7fff907276cc)
    at /home/jonathan/Code/comm-central/mozilla/netwerk/base/src/nsSyncStreamListener.cpp:160
#11 0x00007f7ea4b5d7c4 in nsSyncStreamListener::Read (this=0xf, 
    buf=0x7f7e80e7f000 "", bufLen=4096, result=<value optimized out>)
    at /home/jonathan/Code/comm-central/mozilla/netwerk/base/src/nsSyncStreamListener.cpp:178
#12 0x00007f7ea5443293 in unsigned int NS_ReadLine<char, nsIInputStream, nsCAutoString>(nsIInputStream*, nsLineBuffer<char>*, nsCAutoString&, int*) ()
   from /home/jonathan/Code/objdir-comm-central/mozilla/dist/bin/libxul.so
#13 0x00007f7ea543783f in nsMsgDBFolder::GetMsgTextFromStream (
    this=<value optimized out>, stream=<value optimized out>, 
    aCharset=<value optimized out>, bytesToRead=<value optimized out>, 
    aMaxOutputLen=<value optimized out>, 
    aCompressQuotes=<value optimized out>, aStripHTMLTags=1, aContentType=..., 
    aMsgText=...)
    at /home/jonathan/Code/comm-central/mailnews/base/util/nsMsgDBFolder.cpp:533---Type <return> to continue, or q <return> to quit---
5
#14 0x00007f7ea56abc4a in NS_InvokeByIndex_P (that=0xf, 
    methodIndex=2423419951, paramCount=1, params=0xffffffffffffffff)
    at /home/jonathan/Code/comm-central/mozilla/xpcom/reflect/xptcall/src/md/unix/xptcinvoke_x86_64_unix.cpp:208
#15 0x00007f7ea51af8e4 in CallMethodHelper::Invoke (ccx=<value optimized out>, 
    mode=<value optimized out>)
    at /home/jonathan/Code/comm-central/mozilla/js/src/xpconnect/src/xpcwrappednative.cpp:3081
#16 CallMethodHelper::Call (ccx=<value optimized out>, 
    mode=<value optimized out>)
    at /home/jonathan/Code/comm-central/mozilla/js/src/xpconnect/src/xpcwrappednative.cpp:2348
#17 XPCWrappedNative::CallMethod (ccx=<value optimized out>, 
    mode=<value optimized out>)
    at /home/jonathan/Code/comm-central/mozilla/js/src/xpconnect/src/xpcwrappednative.cpp:2312
#18 0x00007f7ea51b5021 in XPC_WN_CallMethod (cx=0x7f7e936df800, argc=7, 
    vp=<value optimized out>)
    at /home/jonathan/Code/comm-central/mozilla/js/src/xpconnect/src/xpcwrappednativejsops.cpp:1752
#19 0x00007f7ea61fb3ff in js::Interpret (cx=0x7f7e936df800, 
    entryFrame=<value optimized out>, inlineCallCount=6, 
---Type <return> to continue, or q <return> to quit---
    interpFlags=<value optimized out>)
    at /home/jonathan/Code/comm-central/mozilla/js/src/jsinterp.cpp:4477
#20 0x00007f7ea62062a9 in RunScript (cx=0x7f7e936df800, 
    argsRef=<value optimized out>, flags=<value optimized out>)
    at /home/jonathan/Code/comm-central/mozilla/js/src/jsinterp.cpp:484
#21 js::Invoke (cx=0x7f7e936df800, argsRef=<value optimized out>, 
    flags=<value optimized out>)
    at /home/jonathan/Code/comm-central/mozilla/js/src/jsinterp.cpp:592
#22 0x00007f7ea6206bb4 in js::ExternalInvoke (cx=0x7f7e936df800, thisv=..., 
    fval=..., argc=1, argv=<value optimized out>, rval=0x7fff90729568)
    at /home/jonathan/Code/comm-central/mozilla/js/src/jsinterp.cpp:622
#23 0x00007f7ea619ef71 in ExternalInvoke (cx=0x7f7e936df800, 
    obj=<value optimized out>, fval=18445617617794269632, argc=4294967295, 
    argv=0x7f7ea695e040, rval=0x0)
    at /home/jonathan/Code/comm-central/mozilla/js/src/jsinterp.h:910
#24 JS_CallFunctionValue (cx=0x7f7e936df800, obj=<value optimized out>, 
    fval=18445617617794269632, argc=4294967295, argv=0x7f7ea695e040, rval=0x0)
    at /home/jonathan/Code/comm-central/mozilla/js/src/jsapi.cpp:4854
#25 0x00007f7ea51a9bdb in nsXPCWrappedJSClass::CallMethod (
    this=0x7f7e8969a400, wrapper=<value optimized out>, 
    methodIndex=<value optimized out>, info=0x7f7e95dcf450, 
    nativeParams=0x7fff90729620)
    at /home/jonathan/Code/comm-central/mozilla/js/src/xpconnect/src/xpcwrappedj---Type <return> to continue, or q <return> to quit---
sclass.cpp:1692
#26 0x00007f7ea56ac815 in PrepareAndDispatch (self=0x7f7e94e441c0, 
    methodIndex=<value optimized out>, args=0x7fff907297a0, 
    gpregs=0x7fff90729720, fpregs=0x7fff90729750)
    at /home/jonathan/Code/comm-central/mozilla/xpcom/reflect/xptcall/src/md/unix/xptcstubs_x86_64_linux.cpp:153
#27 0x00007f7ea56abcd7 in SharedStub ()
   from /home/jonathan/Code/objdir-comm-central/mozilla/dist/bin/libxul.so
#28 0x00007f7ea5351457 in Run (this=0x7f7e82ca4370)
    at /home/jonathan/Code/comm-central/mozilla/storage/src/mozStorageAsyncStatementExecution.cpp:164
#29 0x00007f7ea569fd67 in nsThread::ProcessNextEvent (this=0x7f7e9b3364c0, 
    mayWait=1, result=0x7fff9072981c)
    at /home/jonathan/Code/comm-central/mozilla/xpcom/threads/nsThread.cpp:547
#30 0x00007f7ea566fcd1 in NS_ProcessNextEvent_P (thread=0xf, 
    mayWait=-1871547345) at nsThreadUtils.cpp:250
#31 0x00007f7ea4b5d8e6 in nsSyncStreamListener::WaitForData (
    this=0x7f7e88e43400)
    at /home/jonathan/Code/comm-central/mozilla/netwerk/base/src/nsSyncStreamListener.cpp:58
#32 0x00007f7ea4b5d93a in nsSyncStreamListener::Available (
    this=0x7f7e88e43400, result=0x7fff9072987c)
    at /home/jonathan/Code/comm-central/mozilla/netwerk/base/src/nsSyncStreamLis---Type <return> to continue, or q <return> to quit---
tener.cpp:160
#33 0x00007f7ea4b5d7c4 in nsSyncStreamListener::Read (this=0xf, 
    buf=0x7f7e7e542000 "", bufLen=4096, result=<value optimized out>)
    at /home/jonathan/Code/comm-central/mozilla/netwerk/base/src/nsSyncStreamListener.cpp:178
#34 0x00007f7ea5443293 in unsigned int NS_ReadLine<char, nsIInputStream, nsCAutoString>(nsIInputStream*, nsLineBuffer<char>*, nsCAutoString&, int*) ()
   from /home/jonathan/Code/objdir-comm-central/mozilla/dist/bin/libxul.so
#35 0x00007f7ea543783f in nsMsgDBFolder::GetMsgTextFromStream (
    this=<value optimized out>, stream=<value optimized out>, 
    aCharset=<value optimized out>, bytesToRead=<value optimized out>, 
    aMaxOutputLen=<value optimized out>, 
    aCompressQuotes=<value optimized out>, aStripHTMLTags=1, aContentType=..., 
    aMsgText=...)
    at /home/jonathan/Code/comm-central/mailnews/base/util/nsMsgDBFolder.cpp:5335
#36 0x00007f7ea56abc4a in NS_InvokeByIndex_P (that=0xf, 
    methodIndex=2423419951, paramCount=1, params=0xffffffffffffffff)
    at /home/jonathan/Code/comm-central/mozilla/xpcom/reflect/xptcall/src/md/unix/xptcinvoke_x86_64_unix.cpp:208
#37 0x00007f7ea51af8e4 in CallMethodHelper::Invoke (ccx=<value optimized out>, 
    mode=<value optimized out>)
    at /home/jonathan/Code/comm-central/mozilla/js/src/xpconnect/src/xpcwrappedn---Type <return> to continue, or q <return> to quit---
ative.cpp:3081
#38 CallMethodHelper::Call (ccx=<value optimized out>, 
    mode=<value optimized out>)
    at /home/jonathan/Code/comm-central/mozilla/js/src/xpconnect/src/xpcwrappednative.cpp:2348
#39 XPCWrappedNative::CallMethod (ccx=<value optimized out>, 
    mode=<value optimized out>)
    at /home/jonathan/Code/comm-central/mozilla/js/src/xpconnect/src/xpcwrappednative.cpp:2312
#40 0x00007f7ea51b5021 in XPC_WN_CallMethod (cx=0x7f7e936df800, argc=7, 
    vp=<value optimized out>)
    at /home/jonathan/Code/comm-central/mozilla/js/src/xpconnect/src/xpcwrappednativejsops.cpp:1752
#41 0x00007f7ea61fb3ff in js::Interpret (cx=0x7f7e936df800, 
    entryFrame=<value optimized out>, inlineCallCount=6, 
    interpFlags=<value optimized out>)
    at /home/jonathan/Code/comm-central/mozilla/js/src/jsinterp.cpp:4477
#42 0x00007f7ea62062a9 in RunScript (cx=0x7f7e936df800, 
    argsRef=<value optimized out>, flags=<value optimized out>)
    at /home/jonathan/Code/comm-central/mozilla/js/src/jsinterp.cpp:484
#43 js::Invoke (cx=0x7f7e936df800, argsRef=<value optimized out>, 
    flags=<value optimized out>)
    at /home/jonathan/Code/comm-central/mozilla/js/src/jsinterp.cpp:592
---Type <return> to continue, or q <return> to quit---
#44 0x00007f7ea6206bb4 in js::ExternalInvoke (cx=0x7f7e936df800, thisv=..., 
    fval=..., argc=1, argv=<value optimized out>, rval=0x7fff9072b718)
    at /home/jonathan/Code/comm-central/mozilla/js/src/jsinterp.cpp:622
#45 0x00007f7ea619ef71 in ExternalInvoke (cx=0x7f7e936df800, 
    obj=<value optimized out>, fval=18445617617794269632, argc=4294967295, 
    argv=0x7f7ea695e040, rval=0x0)
    at /home/jonathan/Code/comm-central/mozilla/js/src/jsinterp.h:910
#46 JS_CallFunctionValue (cx=0x7f7e936df800, obj=<value optimized out>, 
    fval=18445617617794269632, argc=4294967295, argv=0x7f7ea695e040, rval=0x0)
    at /home/jonathan/Code/comm-central/mozilla/js/src/jsapi.cpp:4854
#47 0x00007f7ea51a9bdb in nsXPCWrappedJSClass::CallMethod (
    this=0x7f7e8969a400, wrapper=<value optimized out>, 
    methodIndex=<value optimized out>, info=0x7f7e95dcf450, 
    nativeParams=0x7fff9072b7d0)
    at /home/jonathan/Code/comm-central/mozilla/js/src/xpconnect/src/xpcwrappedjsclass.cpp:1692
#48 0x00007f7ea56ac815 in PrepareAndDispatch (self=0x7f7e8ed48380, 
    methodIndex=<value optimized out>, args=0x7fff9072b950, 
    gpregs=0x7fff9072b8d0, fpregs=0x7fff9072b900)
    at /home/jonathan/Code/comm-central/mozilla/xpcom/reflect/xptcall/src/md/unix/xptcstubs_x86_64_linux.cpp:153
#49 0x00007f7ea56abcd7 in SharedStub ()
   from /home/jonathan/Code/objdir-comm-central/mozilla/dist/bin/libxul.so
---Type <return> to continue, or q <return> to quit---
#50 0x00007f7ea5351457 in Run (this=0x7f7e7f0cc790)
    at /home/jonathan/Code/comm-central/mozilla/storage/src/mozStorageAsyncStatementExecution.cpp:164
#51 0x00007f7ea569fd67 in nsThread::ProcessNextEvent (this=0x7f7e9b3364c0, 
    mayWait=1, result=0x7fff9072b9cc)
    at /home/jonathan/Code/comm-central/mozilla/xpcom/threads/nsThread.cpp:547
#52 0x00007f7ea566fcd1 in NS_ProcessNextEvent_P (thread=0xf, 
    mayWait=-1871547345) at nsThreadUtils.cpp:250
#53 0x00007f7ea53a26ed in nsBaseAppShell::Run (this=0x7f7e9b3d1fd0)
    at /home/jonathan/Code/comm-central/mozilla/widget/src/xpwidgets/nsBaseAppShell.cpp:183
#54 0x00007f7ea5293fee in nsAppStartup::Run (this=0x7f7e937d8640)
    at /home/jonathan/Code/comm-central/mozilla/toolkit/components/startup/src/nsAppStartup.cpp:191
#55 0x00007f7ea4b2c244 in XRE_main (argc=<value optimized out>, 
    argv=<value optimized out>, aAppData=<value optimized out>)
    at /home/jonathan/Code/comm-central/mozilla/toolkit/xre/nsAppRunner.cpp:3673
#56 0x0000000000401a16 in main (argc=5, argv=0x7fff9072c308)
    at /home/jonathan/Code/comm-central/mail/app/nsMailApp.cpp:101
(gdb)