Permissions, PRAM, or re-installing the OS will not do anything for the battery.
When you use Disk Utility to repair disk permissions, it reads the Bill of Materials files from the initial Mac OS X installation and compares its list to the actual permissions on each file listed. Therefore, you should repair disk permissions, if you experience symptoms that indicate permission related problems after installing software, software updates, or applications not hardware issues like a battery.
PRAM stores certain system and device settings in a location that Mac OS X can access quickly. Exactly which settings are stored in the computer's PRAM varies depending on the type of computer as well as the types of devices and drives connected to the computer. Some information store in PRAM includes: display and video settings, startup volume, speaker volume, recent kernel panic information, & DVD region setting.
I would check your Console, it can be found here: /Applications/Utilities/Console.app
Select All Messages and search for shutdown. You should see a message "Previous Shutdown Cause: "
If you see any of these causes take your computer to the Genius Bar, they can get you a new battery. If you don't see any of them still take it to the Genius Bar because they can look at the shutdown causes and find out why it is shutting down, and also run battery diagnostics on the battery.
Shutdown Cause: 0 = Battery/Power disconnected: Normal behavior if battery was removed while system was on and no other power source connected.
Shutdown Cause -60 = Battery fully drained: Normal behavior if unit was left asleep on battery for too long.
Shutdown Cause -103 = Battery cell under voltage detected.
Shutdown Cause -74 = Battery temperature exceeds 65C for 3 milliseconds
Shutdown Cause 2 = Battery is fully discharged