My Pokémon game keeps auto-resetting

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I was playing Pokemon Sapphire, and I encountered a glitch of some sort. While I was in the middle of a Pokemon battle, my GBA SP decided to randomly automatically restart.
At first, I thought it may have been due to an old system, however it continued repeatedly. I switched the game into a DS Lite, and that did not fix anything.
I was able to figure out that the auto-reset only occurred when I switched out to specific Pokemon, Gardevoir for example. Has anybody else encountered this issue?
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