Here's my yeast reuse process:
I buy a vial of yeast, make a starter and make a beer. After kegging I dump some of the yeast cake into a mason jar and put it in the fridge for later. I dump some of the yeast cake down the sink if there's still too much in the carboy. Then I put fresh wort on the remaining yeast cake. I make about 10 batches altogether (sometimes less if I tire of that strain), dumping out some of the excess yeast each time. After the last batch I clean the carboy thoroughly so it's ready for the next series. When I'm ready to start a new series, I grab my harvested yeast from the first batch out of the fridge, make a starter and repeat the process. If I don't get around to using the harvested yeast within 8-12 months or so, I will decant the old beer and put some fresh wort in the jar. By harvesting from the first batch of each series, I can squeeze the maximum number of batches out of one vial before I feel like I'm pushing the generational limits and buy new yeast. I don't think I've ever bought the same yeast twice.