We are on gen 12 with our house ale strain at our 5bbl brewery. I'll propagate new yeast after G15. Taking it out this far requires excellent sanitation and harvesting practices though. I don't take lager yeast past 6gens. Part of the reason breweries can do this is because we can crop the select layer of yeast from the cone immediately after terminal gravity has been reached. Beer is a horrible, waste-filled environment for yeast and viability drops pretty quick.
As a homebrewer, I've gone out 8gens or so with ale yeast. Probably could have gone further but I didn't brew frequently enough to keep the yeast happy. Part of the reason I was able to consistently do this with good results and healthy yeast was my yeast harvesting/propagation practice. I never harvested yeast from the cake. I harvested it from the starter. I would make my starter larger by about 150-200B extra cells and harvest at that point. Crash cool in a mason jar, rack off starter wort/beer, and rinse with sterile distilled water.
Next time I needed to brew, I would create a starter using the harvested yeast from the previous starter and do it all over again. Looking at the cells under a microscope showed very healthy yeast with excellent viability. Almost better than the vitality/viability of the house yeast in my brewery.
IMO, yeast starts to really hit its stride after G3.