If a player made exactly one move's progress in each "no progress" period for 33 moves it would be vanishingly unlikely that this happened by chance. He would have to have a valid method of mating that just happened to be 50 times slower than optimal. In that case he would know how to do it (just not how to do it very fast).
There are perfectly valid methods of playing various endgames that are considerably slower than optimal. KRK shouldn't take more than 16 moves, but in the following example White uses a perfectly valid mating technique, but around three times slower than optimal (against Black's defence).
Mammoth games where the stubborn player is playing randomly would effectively not occur even in the absence of claims under the repetition rule because the probability of surviving n draw claims would decrease exponentially with n.
White's method is in fact three times slower only against the defence used by Black. Had Black played accurately the method would have been only one and a third times slower than optimal. Here is the same method played from the same position against the Nalimov EGTB.
I see. Though I think it would either be no progress at all, or continuous progress. U either know how to do the mate or don't no how to. I think even the most ambitious players would give up if they didn't know how to do it after so long.