This is probably an internal battery problem. I've read that the way the GBA games save data, the battery in the cartridge is prone to burning out after a huge amount of saves. If you want to play FE7, emulation is a good option. It won't have the portability of an SP, but you can play the game.
Sorry to hear your cart isn't saving. I'm kind of at a loss on the specifics on how to troubleshoot problems on old cartridges, so if it isn't the internal battery, sorry I can't help.