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.
In general, I've had more success with the silver oxide batteries over the alkaline ones. But I don't shutoff the camera when on an outing as I forget to turn it on at times. This causes me to lose spontaneous shots at times. I would guess that the front exposure meter button can be pressed in the camera bag causing battery drain.
I've also recently sent in my RTSII to Kyocera of NJ for a CLA (they call it a complete overhaul) plus a mirror repair. I hope they have resolved any electrical issues if any with this camera after the extensive cleaning and testing...