That's the one thing I like about my Garmin Forerunner 405Cx now that it's basically useless as a GPS - it presumably won't die and need a new battery in the kind of time frame most digital watches would. I wonder how many recharge cycles it's actually good for but not intensely enough to have made any attempt to find out yet.
Maybe now would be a good time for me to get a new Garmin, but either way (Garmin or non-Garmin) a rechargeable stop watch might be a good replacement for the dead one.
Does that even exist outside of the realm of GPS watches? I certainly find watches dying on me and needing to go out and buy a new battery more annoying than having to recharge my watch but I could see the rechargeable battery being expensive enough to make people like me a very niche market, outside of those who actually need a GPS.
Does it exist? I'm really not sure but I'm leaning towards getting a new GPS watch. Even the old one isn't completely broken, it is considerably less than fully functional.