Several users have reported an issue in which the iPhone's Mail application suddenly fails to retrieve new messages, generally after switching from one connection method to another (e.g. WiFi to EDGE or vice versa).
As desribed by one Apple Discussions poster:
"If I switch from edge to wifi or visa versa, the phone will no longer retrieve new mail without me doing a restart. It seems whatever mode it's in on startup won't let go of the control of mail until a restarts.
"Last night I was using WiFi and receiving mail fine. Early this morning I turned WiFi off as I was going out and would not have WiFi access. A few minutes ago, back at home, I switched WifI back on and got a flood of several emails from as early as 10:30 this morning."
The only genuine workaround for this issue appears to be a full restart of the iPhone. Hold the sleep/wake button then slide to power off the device, then turn it back on.
Alternatively, you can try force-quitting the Mail application by launching it (if it is not already active) then holding the home key for several seconds until the Mail app disappears and you are returned to the home screen.