Xperia X10 :: Turns Off When Using Internet Through Carrier But Not Through WIFI

I have a strange Issue with my phone Xperia X10. When I use the Internet through the Carrier (3G) for several minutes, and the battery is less then (~80%) the phone simply turns off unexpectedly for no reason. If I then try to turn on the phone it will immidiatly shut down again so quickly I dont even have time to unlock it.

I can use the phone fine, Including connecting to the Internet through WIFI, and I will not have the issue. I can also use the 3G Internet fine until I get to about 80% battery, then the phone will turn off. If I disable the Internet connection through the carrier before I get to 80% I can continue using the phone without problems and even browse the Internet through WIFI. If I connect to the 3G Internet with my battery on less the 80% the phone will Immediately shut down.

I tried doing a full reset and reinstall through the SE PC companion, but it didnt help. I also tried installing a custom ROM and chose Wolfs TW Gingerbread but it didnt help and I still have the exact same issue.