Known problem. There are many threads on this (did you try a search?)
What you can 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 trick above will restart the crashed process (as will a restart), but after some time (minutes or hours) it will crash again. It's a bug Apple created with iPhone 5 push software. It apparently works fine for other models.
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.
I'm agree, Apple must do something, It works on my iPhone 4s with IOS 6.1.2. But it crahs on my brend new iPhone 5. May we should made a bad advice on facebook and tweeter to Apple make a fix?
I'm so disapointed of my iPhone 5! I can't imgagine Apple will do nothing, it still works for my hotmail account !!
I just don't understand!