Hi Gary,
I don't have an RTS II, but do have a couple of FR I's which seem quite similar regarding function and operation. The battery will last over 5 years in my experience. Current draw, no lens, body cap is 10 ma. With the battery check, frame counter switch depressed the current draw goes to 230 ma.
The RTS II does have an exposure lock, which may increase current draw if it's left on all the time and an electronic self timer which could also wear down a battery, I'd imagine. I'd check both areas if your current draw seems excessive.
The shutter is notoriously easy on batteries since it uses a quick pulse to open and another quick pulse to close, really great for long time exposures as there is low draw while the shutter is open. Really a plus in astrophotography. Perhaps all cameras work similarly, I don't know. I hope this helps in resolving your dilemma.
Best wishs,
Happy Holidays,
wojo