Sorry, I was typing in a hurry. Let me clarify:
We have a number of iphone 5's with push email and volume issues.
I will focus on the email issue since it is more pressing that the volume one. Basically push email will not work and the only way new email arrives is by opening the email app manually.
*push is supported on the server as we have many working iphones.
Things we tried:
-checked push settings
-tried removing and adding the account
-tried wiping the phone, restoring from icloud
-tried wiping the phone and adding the email account without restoring from the cloud in case the bug was also being restored.
-tried bringing one of the devices back to Apple, they were kind enough to replace it. Same issue.
-tried all the above all over again with the replacement.. still didn't work.
-searched around a bit and found a possible fix having to do with changing the year but did not work either.
I am not an IT person by any means, but I have been through the exact same issues. Had a 4 and iPad 2. Never an issue until upgrade to the 5. I have spent several hours on phone with Apple Sr Advisor. Final response was "yes, we have a problem and engineering is working on a solution." There was no mention of when a fix will be available. I have seen reports from people running beta tests that say it now works on Wi Fi and LTE but stops when LTE switches to 3G. I have no idea if that is true.