With older battery backed design, when the battery died it was a simple matter of opening the cart, desoldering and removing the battery, looking for a new battery (usually CR2032) with solder tab, and putting it all back together.
With modern console, EEPROM are used in place of battery and SRAM. The EEPROM are good for a finite number of rewrites before it can no longer be rewritten at all. With external memory card, it's as simple as getting another one, transferring all the save games*, and then discarding the old memory card.
But some N64 and most GBA games uses built in EEPROM for save games. When it stops working, then what? Most electronic supplier don't carry soldering tip small enough to deal with SMD chip with tiny leads. There is a special soldering iron attachment that can be used to desolder a larger SMD. (GBA often uses serial EEPROM and may have only 5 or 6 leads in this tiny package)
Assuming one can remove the old chip, where would one find a new EEPROMs? Most mail order catalog carries them but they usually have a minimum order limit and there's no reason to order 20 or so EEPROMs just to meet the limit especially considering not all game uses the same EEPROM type or size.
*a few games like Phantasy Star Online for DC and GC is locked and won't allow copying so that presents another challenge especially for GC owners. DC owners can use web broswer and use the email feature to force copy the save game. Worked for me. GC could get around that if the user used the SD adapter and SD card but they're still vaporware.
EDIT: I could use a spell checker in this forum!