Dry yeast has improved in quality and choices have expanded significantly since seven or so years ago when I started. You absolutely can harvest and re-pitch subsequent generations of dry yeast....and of course liquid yeast. I plan on harvesting some 34/70 when my Oktoberfest is finished and re-pitching in a series of subsequent lagers.
I've taken it out to seven generations before.
I have no real data to back it up but I've read(somewhere)and in my experience certain yeasts with strong characteristics, phenolics, etc may lose some of their character on subsequent pitches...e.g. 3068 and saison yeasts.
Regressing toward a more mundane mean.
How the classic older breweries such as Weihenstephaner maintain quality and yeast character over centuries is amazing. It must involve microbiology and genetic laboratories and using slants to identify single organisms/colonies with desired characteristics /with significant quality control.