js - just note that your right shifter is probably compatible with Shimano rear derailleurs (regarding the amount of cable pulled per gear change), and is probably NOT a 9-speed shifter, but rather a 6- or 7-speed shifter.
The X-7 shifters mentioned above are 9-speed shifters, requiring a 9-speed rear gear cassette and 9-speed compatible rear derailleur. They also work only with SRAM "ESP" cable pull style rear derailleurs. Thus, you would need to buy new shifters, a new rear derailleur, and new rear gear cassette (and perhaps new rear wheel if yours does not have an 8/9 speed hub).
SRAM does make some somewhat better-quality grip shifters for Shimano rear derailleurs, but I'm not sure if they will last longer in your application. Their "Attack" line includes some Shimano-compatible shifters (and some ESP compatible).