Barring every idea mentioned, at this point, I would be suspecting a flaky counter chip, or something's up with the power supply voltage/regulation.
That phototransistor pulse source for a clock input, as it is, is not the best design, but it does work for the other counts, so it is hard to fault it as the cause of the problem. I still don't like it. It wouldn't hurt to try a substitute external pulse source with bounceless, fast rise and fall edges, though, before replacing parts. Clock inputs are very sensitive to bounces and slow edges and strange things can happen with them. If you don't have a clean external pulse source, try putting a buffer between the phototransistor output and the counter clock input that has Schmitt trigger input, such as a 4093 or 4584.