My first Gen iPod does the same thing, it turns on and off until the battery is completely drained. The only way I can keep it on sometimes is if I am letting music play or using an application but once I stop then it starts shutting on and off again. Also I noticed the best way for my to turn it on sometimes is to actually plug it into my MacBook and let it connect to I tunes.
I was really pissed when this problem first occurred but now I have a second Gen I pod touch and A iPhone 3GS and I don't have any problems. I really think Apple restructured the internal format of the device but if anyone has a suggestion of how to fix the turning on and off problem I would really appreciate it.