This is a reoccurring problem and every time I speak to Verizon they throw their hands up and say "it's not us" and refer me to Apple where Apple says "it's not us" and refers me back to Verizon - kind of like Ultimate Ping-Pong.
To start: I work in IT - specifically with mobile devices so I am well versed in technical support -- I have an AT&T iPhone 4 and a Verizon iPhone 4S. Both are set up exactly the same with an iCloud mail account; both have full signal and a 3G indicator. When email is delivered it is pushed to the AT&T iPhone 100% of the time - the Verizon iPhone however only seems to get push email under the right set of variables. If the VZW iPhone has been on more than a few hours push will not work - email isn't retrieved unless I open the Mail app - then all of a sudden the connection refreshes and I have mail - this can be resolved if I power off and back on the device - once a power cycle is complete push again works on the VZW iPhone...but only for a few hours. It is as if after a period of time the phone stops connecting with 3G data in the background. It is definitely not a device issue as the device has been replaced; also I've already done all of the normal troubleshooting by wiping the phone; resetting to factory settings; checking all of the settings on the phone; verifying there are no outages or issues. Anyone have any ideas?
I'm having the same problem! Restarting the phone used to help but not anymore! I've reset the phone, restored, and had it replaced by Verizon. It's just something to do with the Apple \ Verizon software and will have to wait until they fix it. A very annoying bug!