I saw your recommendations on another post from Superclay. Trust me buddy, I've tried everything. I even got a new iphone 5 from the apple store today....nothing, still the same thing. Works for like 5-10 minutes then just stops. I just went back to my 4S which works perfectly. Guess I'll have to wait until Apple comes out with a fix...this is BS.
This is all not necessary.
All you need to do is turn Airplane Mode ON, wait 10 secs or so, then back OFF. Don't bother re-creating accounts, restoring, etc. It's a waste of time and will NOT fix anything.
The problem is a crash of an iPhone process that handles Exchange push over cellular. You cannot fix it yourself. The tricks posted will restart the crashed process, but after some time (minutes or hours) it will crash again. It's a bug Apple created with iPhone 5 push software.
If you want to confirm the crashes:
Look for apsd_date, where date is the date and time of the apsd (Apple Push Service Daemon) crash. If you have one or more of these, you have the problem.
Apple has to fix it with an iOS update. Many of us have opened support calls and Apple is aware of the bug and are working on it.