What the OP is describing doesn't sound like routine out-of-round or off-center issues. The chain goes from tight to not tight permanently. A good whack and it goes to ridiculously loose.

Something is clearly slipping. I'm guessing he has QR that's not holding sufficiently. Yes, I know that QR is perfectly adequate for riding fixed. I'm king of the you-can-ride-fixed-on-QR-hubs fan club. Nevertheless, it seems pretty clear that something is slipping. I'm guessing a QR that can't tighten down sufficiently, isn't being tightened down sufficiently, or has aluminum surfaces instead of steel.

Here's a little experiment. Get a fine-tipped sharpie and draw a small mark at the back and front of the nut/QR skewer where it meets the dropout. Whack at the cranks. Has the wheel pulled forward?