Auto shutdown after about 15 minutes I have a HTC G1 Dream device. I noticed that it has a problem. 

When I unplug it from charger, about 15 minutes later it shuts down.

Is there any solution for this? 

P.S Factory reset won't help here. I've tried this about 3 times.
Sounds like a bad battery, use logcat or a battery monitor and see what happens when it shutdown.

I had a device that would do the same but it would last 2 hours instead and under load would go about 5 mins :p
A new battery sorted it out in the end. But if you can get a new phone as once the battery starts to go the other compentnets will fail as well. If you cannot afford to do by a new phone at least backup on TB on a EXTERNAL SDCARD. so if worse comes to worst you have all the data for all your apps.