I used to have a 2nd generation iPod Touch, and had it connected to my email account at work (Exchange 2003). The iPod got push email as expected, and would often ping before Outlook (2010) would on my PC. I have since upgraded to a Verizon iPhone 4, and it does not get push email, or anything else from Exchange. I've deleted and re-added the account on the phone, and have verified that the delivery setting under Settings is set to Push. If I open the Mail app, then it gets email just fine. It won't even fetch it on its own; I have the interval set to 15 minutes, but I've never seen it receive email without the Mail app open.
Is anyone else experiencing this? Is it a bug introduced in the Verizon iPhone's branch of iOS?
I'm currently running iOS 4.2.8 on it.
UPDATE: I got some logs off of the device, and have found this error a few times:
(date and time) unknown dataaccessd[47] : EAS|connection died with error Error Domain=NSURLErrorDomain Code=-1004 "Could not connect to the server." UserInfo=xxxxxx {NSErrorFailingURLStringKey=https://x.x.x.x/Microsoft-Server-ActiveSync?User=xxxxxx&DeviceId=xxxxxxx&DeviceType=iPhone&Cmd=Ping, NSErrorFailingURLKey=https://x.x.x.x/Microsoft-Server-ActiveSync?User=xxxx&DeviceId=xxxxx&DeviceType=iPhone&Cmd=Ping, NSLocalizedDescription=Could not connect to the server., NSUnderlyingError=0x2f17f80 "Could not connect to the server."} 0x2f2cf20
In the links in the answer posted by berberich, Ping is discussed as a command that the device issues to the server in the process of negotiating the push (if I understand correctly).