Does the problem occur in all the games you own, or just one? Does that trigger feel like it responds differently than the L2 trigger? If it only occurs in some games, it may be a software glitch, in which case you can try reinstalling the game if its installed on your system, or try a different copy of the game to rule out a disk defect.
If it feels different than its counterpart on the left side of the controller, then the spring may be the issue. If you play alot of shooters, especially ones that use the R2 trigger, the spring may have just warn down over time.