He doesn't lose anything, short of you guys not finishing the run. If you finish it you're guaranteed loot, no matter how long it took, and he still gets the depleted stone (which he can attempt to reignite by just doing the same run and doing it fast enough).
Your mythic keystone is never wasted for the week until you literally brick wall into something you actually just can't beat.
Like, if you do Mythic +5 with my keystone, and we win, I get a Mythic +6 and we get loot. If we fail, I get the same keystone back and we get loot, the only difference is now I have to run it again to try for the +6 (and you don't get loot on that subsequent attempt to prevent obvious farming exploit).