Wouldn't be 100% applicable in your case, but this side story should get you thinking. Years ago has a card that wasn't being read by a router correctly, but other cards could, so bad card. But it worked in another router. The issue was both the card and router; the card was a bit worn and had a spot that wouldn't make good contact. That same pin was bent on the bad router. With good cards, it could still make contact, but it was warn just enough with the bent pin it couldn't make contact. Unbent the pins a bit and it worked fine.
Might be a bad pin on that Gameboy. Could be a combo of cart and gba, or if the cart uses something the other carts don't, then it'd be like monjici was saying. When the program tries to access the chip over the bus, he has a poor connection and dies.