You're not alone.
Email is not reliably being pushed to my iPhone. If the mail.app is not running in the background, it fails to push. If the mail.app is running in the background, it will occasionally push, often with a delay.
I am also experiencing sporadic problems with incorrect password prompts with the OS X mail.app when sending and receiving.
I'm not yet certain if the issue is related to iOS 5 or 10.7.2 or just due to the overwhelming crush of new users and volume of traffic.