Upgraded to APC 3.1.13.  No change, still segfaulting.  Upgraded to latest kernal:
Linux 3.2.0-26-generic #41-Ubuntu SMP Thu Jun 14 17:49:24 UTC 2012 x86_64 x86_64 x86_64 GNU/Linux

Program terminated with signal 11, Segmentation fault.
t#0  0x00007fc6d9d4330d in do_bind_function (opline=0x7fc64eac5ab0, function_table=0x7fc6de5a2a90, compile_time=0 '\000') at /build/buildd/php5-5.3.10/Zend/zend_compile.c:2978
2978	/build/buildd/php5-5.3.10/Zend/zend_compile.c: No such file or directory.
(gdb) bt
#0  0x00007fc6d9d4330d in do_bind_function (opline=0x7fc64eac5ab0, function_table=0x7fc6de5a2a90, compile_time=0 '\000') at /build/buildd/php5-5.3.10/Zend/zend_compile.c:2978
#1  0x00007fc6d9d81bbc in ZEND_DECLARE_FUNCTION_SPEC_HANDLER (execute_data=0x7fc6d7601e50) at /build/buildd/php5-5.3.10/Zend/zend_vm_execute.h:586
#2  0x00007fc6d9d8193b in execute (op_array=0x7fc6de8f0800) at /build/buildd/php5-5.3.10/Zend/zend_vm_execute.h:107
#3  0x00007fc6d9d5cea0 in zend_execute_scripts (type=0, retval=0x8de63e558, file_count=3) at /build/buildd/php5-5.3.10/Zend/zend.c:1308
#4  0x00007fc6d9d09513 in php_execute_script (primary_file=0x0) at /build/buildd/php5-5.3.10/main/main.c:2323
#5  0x00007fc6d9dec3ad in php_handler (r=0x7fc6d9dec3ad) at /build/buildd/php5-5.3.10/sapi/apache2handler/sapi_apache2.c:688
#6  0x00007fc6de04d508 in ap_run_handler ()
#7  0x00007fc6de04d97e in ap_invoke_handler ()
#8  0x00007fc6de05cbdc in ap_internal_redirect ()
#9  0x00007fc6d7fe4635 in ?? () from /usr/lib/apache2/modules/mod_rewrite.so
#10 0x00007fc6de04d508 in ap_run_handler ()
#11 0x00007fc6de04d97e in ap_invoke_handler ()
#12 0x00007fc6de05d570 in ap_process_request ()
#13 0x00007fc6de05a398 in ?? ()
#14 0x00007fc6de053fa8 in ap_run_process_connection ()
#15 0x00007fc6de0621d0 in ?? ()
#16 0x00007fc6de06293a in ?? ()
#17 0x00007fc6de0634e7 in ap_mpm_run ()
#18 0x00007fc6de0384a4 in main ()


However, it is not including a different file.  Some are still nap.ctp, while others are social.ctp.  Each one is when a function is defined:
[0x7fc6d7601e50] ??? /.../social.ctp:58 
[0x7fc6d7600dd8] ??? /.../view.php:1159 

social.ctp:58
57: if(!function_exists('iconCreate')){
58:        function iconCreate($imgName, $iconClass, $icon_set, $icon_set_path){


Also, this appears to happen most at 1:30-1:40AM server time, and the servers impacted are random between WEB13 and WEB27.   With some sporadic segfaults during the day. 

[Wed Mar 26 01:39:18 2014] [notice] child pid 18776 exit signal Segmentation fault (11)
[Wed Mar 26 01:39:33 2014] [notice] child pid 18761 exit signal Segmentation fault (11)
[Wed Mar 26 01:39:38 2014] [notice] child pid 18781 exit signal Segmentation fault (11)
[Wed Mar 26 01:40:16 2014] [notice] child pid 18759 exit signal Segmentation fault (11)
[Wed Mar 26 01:40:40 2014] [notice] child pid 18767 exit signal Segmentation fault (11)
[Wed Mar 26 01:42:31 2014] [notice] child pid 18773 exit signal Segmentation fault (11)
[Wed Mar 26 01:43:49 2014] [notice] child pid 20663 exit signal Segmentation fault (11)
[Wed Mar 26 01:44:11 2014] [notice] child pid 20505 exit signal Segmentation fault (11)
[Wed Mar 26 01:45:31 2014] [notice] child pid 18779 exit signal Segmentation fault (11)
[Wed Mar 26 01:46:04 2014] [notice] child pid 20481 exit signal Segmentation fault (11)
[Wed Mar 26 01:46:37 2014] [notice] child pid 32282 exit signal Segmentation fault (11)
[Wed Mar 26 01:47:02 2014] [notice] child pid 23009 exit signal Segmentation fault (11)
[Wed Mar 26 01:47:04 2014] [notice] child pid 23006 exit signal Segmentation fault (11)