The battery of my Galaxy S 2 is draining very quickly...including on plane mode
The Android Authority has a great article on ways to extend your battery life on the S2.  

In my experience:


Live Wallpaper is a huge battery eater  
When I'm at work my 3G signal is very weak inside the building, which completely kills my battery in about 4 hours.  I've found that if I leave the Wi-Fi connected at work and at home, the phone won't constantly look for a 3G signal, thus saving my battery.
Turning down the screen brightness is also a big help


If you've tried all these suggestions with no improvement, you might consider trying  JuiceDefender.