With your specific situation, it may be posture related. I notice if I take more than 10 putts without backing away and resetting, my posture starts to settle. Even a good putting position would be hard to hold for too long without a kink getting tossed in somewhere. Walk around some, and keep at it. I don't think there's such a thing as too many putts, but I think holding one position for too long without a break is a real thing.