Well even I experience similar battery life. Even on a new battery, I have to charge it by 11PM. Though I do use Wifi for an hour, some gaming, heavy mail usage and lots of calls.
Off late I have been experiencing random restarts but I think that is more to do with the moisture that seems to have hit the power button. I could be wrong.
Now coming back to your query, I doubt that the official service centers will take up your case. You can probably try out the local service centers. Have you tried a factory reset though? Maybe some app is causing this problem of instability.