This is NOT a carrier issue.
First if all, there’s no way the carrier can delete messages from your messages app. Second, after a reboot the messages come back. So please stop with the take it up with the carrier nonsense. This IS an iOS problem.
Secondly, I’m having the exact same issue but it happens with BOTH (gasp!) iMessage and SMS.
My text messages would show up for a split second and then disappear; Green bubbles for SMS and Blue bubbles for iMessage would quickly vanish after I sent them. This problem started happening after my phone lost sync with date/time (I changed the date to 2012 accidentally). I reset the date and time and now messages don’t disappear anymore.
There were also problems loading webpages, I would always get “Safari Can’t Verify the Identity of the Website” This occurred because the system clock and date was not the current date, so SSL certificates were being considered invalid. These messages stopped after I fixed the date/time.
Here is a guide I followed:
Confirm the System Time is Correct
· If you’re still having the problem, your time settings may be off. Yes, time, as in the clock on the computer. If that’s the problem, it’s quite easy to resolve:
· Be sure the iPhone has active internet access, this is necessary to retrieve accurate date and time info from Apple servers
· Quit Safari
· Open the iPhone settings menu and go to General
· Choose “Date & Time” and check the box for “Set automatically”
· Relaunch Safari
You should be good to go with no more verification errors. This works for situations where the system time is reporting as vastly different than what is expected from the remote server, like if a computer is reporting itself from the future.