That sounds like a dead battery to me - when you remove the cartridge the SRAM is no longer powered - so while you were able to save while it was powered, the battery is not keeping it powered once it's removed. I would test it and make a save game file, leave it in the GBA and leave it overnight and see what happens.
Pokemon Gold is getting old enough that there's a very good chance the original battery isn't doing so hot any more. I believe that generation of Pokemon especially had battery issues due to the real-time clock.
This is not directly helpful and you may have considered it already, but have you thought about using an emulator to play the game on your phone ?
I did this recently on my S3 and the controls translate well to touch-screen use. The ROMs are very small, too ! The GBC ones are only ~2Mb and GBA are usually 5-10Mb. Transferring my games to my phone was just another way to consolidate and make life simpler / more fun / easier.
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