Seems like this is quite common from what I've experienced and read here. Even with a new, tested working 5k pot, sometimes in the middle of a game, the calibration will get all screwy. IIRC, Jowseph mentioned this happens to him, too.
At the beginning of most delivery days, I sweep the handlebars to the extreme left and right before heading up the street to sort of "recalibrate" the controls. I'm not sure if it actually does anything, but it seems to improve the centering.