If you are rinsing yeast properly, with the most sanitary conditions possible, there is almost no limit to the number of times you can reptich yeast. Genetic mutations are fairly rare, and even more rarely do these mutation not result in cell termination. Some scientific studies have shown that after several hundred repitches in a commercial brewery, that the yeast slurry was still identical to the original strain.
When I say properly rinsing, I mean that you are not causing a 'selection' on the type of yeast in the slurry by your process. This is by far more detrimental to yeast characteristics than the remote chance of a genetic mutation. For instance, if you select yeast off the bottom before fermentation is done, you are likely selection for a yeast with a higher flocculation than the original yeast strain as a whole. In just a few generations of this selection, you will eliminate the average and low flocculent yeast cells and only have the high flocculent yeast cell left. The opposite would be true if you only harvest from secondary, where only the least flocculent cells will remain from your selection.
You want to make sure you are selecting the largest sample possible (like the whole cake after cold crashing) in order to encompass the largest span of variability within the yeast strain. When you let the slurry settle out, as soon as you see some separation pull the top clear layer off and discard, and pull the yeast layer off the hops and break material. This will help minimize selection pressures by not allowing highly flocculent yeast to settle out before the next step.
Bacterial or yeast contamination is another issue. I minimize this by sterilizing all my flasks, jars, water, funnel, wort and anything else I can in a pressure canner. I also do all my transferring in a close room, with no vents, and I spray a lot of the bench/table down with 70% EtOH. There will always be some bacteria and wild yeast in beer, this is inevitable because of our process and limited resources for expensive sanitary conditions. But we can takes steps to drastically limit that contamination.
A lot of people see these steps as too burdensome to bother with, but the rewards can be seen in just a few repitches. The vials/packs you buy from the store were grown in a lab and not in anything resembling beer. So, it takes a couple of rounds of beer fermentation for the yeast to start fermenting in the way they were intended to. If you simply use the vial and dump, then buy another for the next batch, you never really get the results of good beer fermentation. This is only possible from rinsing and reusing yeast. Most yeast experts will say that a fresh vial/pack really takes 3-4 beer fermentations before they start chugging along nicely and giving their intended results.
You can test this idea by making the same exact batch 3-4 times in a row; same temp. fermentation, same pitch rate, everything the same except the rinsed yeast generation. Then at the end, taste all the beers side-by-side. You will probably see a big difference in the beers.
Save me, O God! For the waters have come up to my neck. - Psalm 69:1