Perhaps they had problems with making the backup battery terminals fit inside the calculator, or that the backup battery was causing problems with the RAM. Either way, they intended to have one but it didn't happen.

Yeah my 81 has a round space where would be a backup battery, but none can be inserted. By the way how long are those batteries supposed to last? In NES games some of my batteries have lasted for 25+ years and still keeps my saves fine, while some other NES or even SNES games had dead batteries after only 3 years. Also TI says to replace the battery after 3 years, yet mines worked fine for nearly a decade in some cases.

It's possible that the backup battery has been changed at some point before you had the calculator. Unless it's a family heirloom or something.

I don't think I've ever changed the backup batteries on any of my calcs. I don't use my oldest ones anymore, and I don't even remember if they still remember the memory contents. I think if the main batteries are out long enough some of them might do a RAM clear, but they seem to be able to retain it for short periods.

I also have some Game Boy carts approaching 15–20+ years and haven't had any dead saves yet. Never any problems with NES/SNES ones back in the day, either, though Nintendo said they would last 5 years.

Pokemon Gold and Silver last much shorter than every other game in average because the games have an internal clock feature that runs 24/7, draining even more power. The day/night clock feature was removed in 3rd generation games for that reason.

Really? Wikipedia said otherwise the last time I checked (and cited dead batteries as reason why)

Yeah I read now on Wikipedia that day and night is definitively gone. I guess that still leaving a clock in for other purposes still drains the battery fast enough, though. Also the battery problems with 2nd and 3rd gen Pokémon games brings up another question that is more related to calcs: If a TI-84 Plus is left with the 4 AAA batteries removed for a long time, will the small button battery drain faster than older calcs due to the clock?