The Ruins of Machi Itcza I think I understand why it's impossible to collect the 13th key.
Pay attention to the short story that is given before you begin play. 13 magic keys were hidden that when brought together reveal the secret to the meaning of life. The player character collects these keys, and each subset of the 13 is harder/more convoluted to obtain than the last. The very last key is impossible to obtain, because (according to the developer) the meaning of life, if it exists, is impossible to know, or perhaps there is no meaning at all, and attempting to know it is a total exercise in futility (which is why you apparently lose the 12 keys upon entering the center area--you got them all for nothing).
I'm not saying that I agree with it, but that's the message I get from it. Now if my interpretation ain't correct, MNWS, perhaps you need to reconsider your game design philosophy because I honestly have no other explanation for what seems to be arbitrary. Anyway, you get points for the Fridge Brilliance moment, regardless of whether or not it was intentional.
As for the gameplay, I feel that it could have had a greater quantity and quality of puzzles. The only puzzle in the game is figuring out how to dodge the enemies, which only takes a few seconds of thought to solve.
