There is a save battery recharge method that's posted on the here on Serebii on the G/S/C board for people whom own a copy of G/S/C that won't save. Here is the method as posted:

Originally Posted by Domefossil
Internal battery dead? Well don't reach for the screwdriver and spare, for there is an easier way, my friends, tested by yours truly. Just follow these simple and conscise steps:

1. Turn your GBC/GBA/GBA SP with the G/S/C in it on.
2. Start a new game. Set your prefrences.
3. Save at Elm's or early in the game.
4. If you have a GBA SP, (its much easier with one) turn the light off and put it to charge overnight or for a long time.
5. Your G/S/C cartdridge is barely alive, so the best situation would be to play your heart out and keep leaving it on for hours.
6. When you reach 100 play hours, your internal battery shall be fully recharged, and your game should work as normal.

I have personally done this with my Silver Version, and it worked like a charm.
I know this works for many people's G/S/C games, but has anyone tried doing this with the gen 1 games? (Red, blue, green, yellow)

I might test it out myself when my copies of Yellow and Red lose their save function (It hasn't happened yet, I must be really lucky.)

If anyone else has a dry battery copy of one of the first gen games you're welcome to test it out and post your findings here. I'm curious to see if it works.