Firstly thank you for trying my game. You aren't missing anything, that key should stay in your inventory and open the next door. I haven't been able to recreate this bug yet. What browser are you using?
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It could be one or both of the following. Even though my code should allow it, the game won't handle save till you're on the ground and you can go through the door before you touch the ground. Otherwise it could be that godot's queue_free is more aggresive than I thought and removes the key node, and it's methods, before it sends the signal to the gamecontroller to save. For now I just stop the player from being able to access an exit right after getting a key.