I've had a Panasonic DMC-GF2 for a couple of years and the battery life has always been terrible. I've bought a new battery, thinking that was the problem and battery life has still been bad. I will put a fully charged battery in the camera and 48 hours later (with the camera off the whole time) the battery will be dead.
Friends of mine with the same camera have not had this issue. I wish I had identified this problem and returned the camera while it was still under warranty. Am I doing something wrong or did I just get a bad unit?
I have own this camera for 2 years and I don't have battery problem you mentioned. The camera preserve its battery power well even I forgot to switch it off, the camera goes into sleep mode after a while. Although Panasonic has released a newer firmware but the firmware update isn't relate to battery power. So I guess your unit should have some problem and should return it before the warranty expire.
You answered the question yourself by saying that your friends have the same camera with no issues, so you basically confirmed it is most likely and issue with the camera.
As for the previous mention of taking your battery out overnight is a little odd and in all my time doing photography have never come across such a suggestion. In fact, I have one camera that I can leave switched on for days without hardly any decrease in battery because most cameras will go into a form of power saving mode.
If I was you I would bite the bullet and submit a support request to Panasonic and see what they say.