I've changed the battery on my copy of Pokemon Gold twice. I wonder if whoever designed those cartridges expected anyone to still be playing the game twenty years later.
I've seriously considered replacing the SRAM with MRAM so as to not require battery replacement. It would need level shifters though.
Meanwhile my Blue version is somehow still ticking along on its original battery nearly 23 years later.
My red and yellow carts still have original batteries too, and the saved games still work perfectly (as of two years ago when I last checked). The only thing I might say "oh well" about losing is the official Mew I got from some Pokemon event at a mall, but I don't even have the certificate that it came with so it doesn't really matter.
Gen II (Silver/Gold/Crystal) had a time-of-day thing going, which I expect probably required more battery power due to also needing to maintain a clock along with the save data. Gen I only needed to hold the save data. That would be my guess for the difference in battery life.
Flash wasn't cost effective in the 90s, so most save games were stored in RAM with a battery so that it never lost power.
It's for keeping save data =)
And losing it. I’m sure many people are surprised to come back to their GB, NES, and SNES games after a few decades to find that their save files are gone.
I've plugged in SNES cartridges that are 30 years old and the save data still persists. I'm guessing they got the same man who designed the everlasting Casio digital watch battery to design those.
My 33 year old final fantasy cart still holds saves; other newer ones have died. There's a huge variance there.
I was surprised last year to find my saves on Zelda 2 and others were still intact. Zelda 1 had been dead for years though.
I've heard about this for years, but I've never had it happen, and I don't know anyone else who's experienced it. I don't doubt it happens, but what could cause such a discrepancy in the time it takes to degrade?
Different battery manufacturers? Batteries stored in different conditions?
Anecdata
I recently got my old Game Boy games out so my son could play them. They've been in a box in storage for 20+ years. My saved games from the 90s are still there on all the ones I've checked.
Back them up on a old gameshark or something. I lost all my gamesaves and wish I still could revisit them.