General :: Battery Drops Instantly On Data Connection?

i have this strange issue with my old Xperia X10 (about 3 years old, running 2.3.3). The phone runs fine, fully charged can last two days with normal usage (as always). I can play any games for hours before the battery goes dead. But as soon as I turn on data connection, both wifi or mobile network, it runs about 2 minutes and suddenly "turning off" window appears and the phone shuts down. When I start up the phone again, the battery is about 20-30% lower than before the shutdown (depends on the percentage, can drop to zero if charged at 50%) and shuts down again after couple seconds (i can barely type in the PIN code). But if I manage to turn the data connection off again in those few seconds, it doesn't shut down anymore and runs normally again. Weird thing is that in following hour after this incident, the battery slowly recharges itsself back to the original state (or little below it, just as it normally would). Here is the pic:

I guess its not faulty battery or anything, probably its software related but I can't imagine a sw that could drain the battery so fast (in seconds), almost like if it short-circuited the battery.