Many users have reported an issue in which the iPhone's mail application fails to retrieve messags in the background, no matter what checking interval is set and regardless of whether or not push is enabled. An Apple Discussions thread harbors more than 275 posts on the issue.
iPhone Atlas reader Anil Panigrahi writes:
"After updating to the latest iPhone firmware (2.1), many users, including myself, are finding that there is no email fetching while the phone is in standby mode. This is a major concern to many users, business users in particular."
An Apple Discussions poster quips:
"This is the new fix Jobs implemented in 2.1 to fix the battery life"
Fix Some users have now reported that downgrading to iPhone OS 2.0.2, setting up email accounts anew, then updating back to iPhone OS 2.1 resolves this issue.
Visual instructions for downgrading can be found in this YouTube video (embedded below)
and links to old OS versions can be found here.