This is very easy to reproduce for me, on At+t network. Not sure if it's an operator issue, nuntium issue, or udm issue at this point. Here are the steps to easily reproduce it for me:

1) from another phone (phone A), create a Group Chat message to your ubuntu phone and one other phone
2) send 4-5 messages in rapid succession (i.e. "one", "two", "three", "four", "five") from phone A
3) on ubuntu phone, verify that all messages are receivied, otherwise you'll see a message from "Unknown Number" with body "message not found"
Repeat steps 1-2 until you receive the "Unknown Number/message not found" message in messaging app.
For me this happens usually after 2 or 3 cycles

Based on my logs, it looks like download mgr downloads the messages, and nuntium tries to upload a reply (assuming it's an ack reply). This fails according to the nuntium log:

2016/01/11 16:59:59 Starting download of http://166.216.166.67:8006/1113152245600010000030000 with proxy 172.26.39.1:80
2016/01/11 17:00:00 Progress:60 60
2016/01/11 17:00:00 Progress:60 60
2016/01/11 17:00:00 File downloaded to /home/phablet/.local/share/ubuntu-download-manager/Downloads/1113152245600010000030000
2016/01/11 17:00:00 Created /home/phablet/.cache/nuntium/store/9d454e8dff12878113d91725fa5fb3f6.m-notifyresp.ind to handle m-notifyresp.ind for 9d454e8dff12878113d91725fa5fb3f6
2016/01/11 17:00:00 Starting upload of /home/phablet/.cache/nuntium/store/9d454e8dff12878113d91725fa5fb3f6.m-notifyresp.ind to http://mmsc.mobile.att.net with proxy 172.26.39.1:80
2016/01/11 17:00:00 Progress:8 8
2016/01/11 17:00:02 Cannot upload m-notifyresp.ind encoded file /home/phablet/.cache/nuntium/store/9d454e8dff12878113d91725fa5fb3f6.m-notifyresp.ind to message center: NETWORK ERROR

In the corresonding download manager log (using tail -f .cache/ubuntu-download-manager/*), it appears the initial download was correct and I don't see any failures:

//FAILED MMS Message
I0111 16:59:59.504356  1808 manager.cpp:224] Create MMS download == {url: http://166.216.166.67:8006/1113152245600010000030000 hostname:  172.26.39.1 port:80}
I0111 16:59:59.505923  1808 manager.cpp:131] Owner is:  :1.383
I0111 16:59:59.506072  1808 factory.cpp:70] Factory assigns the Download Uuid.
I0111 16:59:59.507314  1808 apparmor.cpp:116] UNCONFINED APP
I0111 16:59:59.507707  1808 apparmor.cpp:185] Local path is /home/phablet/.local/share/ubuntu-download-manager/Downloads
I0111 16:59:59.510921  1808 manager.cpp:131] Owner is:  :1.383
I0111 16:59:59.513485  1808 downloads_db.cpp:366] Insert download
I0111 16:59:59.531574  1808 manager.cpp:119] void Ubuntu::DownloadManager::Daemon::DownloadManager::onDownloadsChanged(QString) /com/canonical/applications/download/ddc0ffa352844cecba4ece5133af86fb
I0111 16:59:59.542951  1808 downloads_db.cpp:363] Update download
I0111 16:59:59.592730  1808 file_download.cpp:355]  Download ID{ ddc0ffa352844cecba4ece5133af86fb } Performing a network download.
I0111 16:59:59.593823  1808 file_download.cpp:362]  Download ID{ ddc0ffa352844cecba4ece5133af86fb } EMIT started(true)
I0111 17:00:00.499265  1808 file_download.cpp:1089]  Download ID{ ddc0ffa352844cecba4ece5133af86fb } Rename ' /home/phablet/.local/share/ubuntu-download-manager/Downloads/1113152245600010000030000.tmp' to ' /home/phablet/.local/share/ubuntu-download-manager/Downloads/1113152245600010000030000'
I0111 17:00:00.501030  1808 downloads_db.cpp:363] Update download
I0111 17:00:00.526609  1808 filename_mutex.cpp:88] Released path ' /home/phablet/.local/share/ubuntu-download-manager/Downloads/1113152245600010000030000'
I0111 17:00:00.526686  1808 file_download.cpp:1102]  Download ID{ ddc0ffa352844cecba4ece5133af86fb } EMIT finished /home/phablet/.local/share/ubuntu-download-manager/Downloads/1113152245600010000030000

The failed .mms file can be found in .local/share/nuntium/store/9d454e8dff12878113d91725fa5fb3f6.mms, which I have attached