No, don't buy a new one. I've had that happen to me twice, in the GT5P era where I raced a lot more with the controller. All the downshifting made my L2 button spring break on 2 of my controllers.
Just find a 3 1/4 diskette, break it and cut the spring so it matches the size of the spring of your trigger buttons. Believe it or not, the springs from diskettes are actually stiffer and thicker, leaving your PS3 controller triggers feeling great.
PROTIP: If your controller isn't under warranty and you're intending to follow this road, change both springs in one go instead of waiting for the other one to break. It'll happen eventually anyways. It is also a great oportunity to thoroughly clean your controller inside and out.