I have the same issue which appears to be router specific and only related to emails from an Exchange server as Gmail works fine.
I have both iphone and ipad which work seamlessly on 3G and the first time I check emails on arrival at home on the wireless network. When I check a second time, the headers appear in the phone / ipad although nothing appears in the body, no matter how long the phone is left.
If you go to airplane mode and back, the symptoms are the same as arriving at home. Works one time and then doesn't.
I have proved this to the router as I purchased a Thompson TG845 (which is awful to setup) and it works consistently. When I install my preferred Netgear routers, the above problem exists even if I set the iphone in the DMZ.
Exceedingly frustrating and it appears as if I'm not the only one to experience this.
Changing the time to manual as suggested had no effect neither did aligning it to the Exchange servers time.
Look forward to anyone with the techo answer.