I have a different slant on thing. I know a lot of brewers collect their yeast from spent wort and recycle it but this is not what I am proposing.
Here is my plan and if folks think differently then give me input.
This is what I would call the beer equivalent of keeping Sour Dough going for the long term. Start a very small wort of only about 3% potential and pitch the yeast in it. Say a cup of water with 2 ounces of German Pils or 2 row. Something that converts easy. Cool it to temp and pitch the yeast in it. Let us say we use Nottingham. It's an easy yeast to check later on for mutation but hopefully that won't happen with the way I am going to go at it. Let it work for until half the sugar is gone and make up another cup of 3% wort and add it to the existing wort. Just enough to feed the yeast and keep it working and happy. Each time you feed it move it to a secondary so that the trub does not accumulate. Do this every couple of days and when it is time to make beer pull off enough to pitch your beer. But keep enough to keep it going. You have never really recycled the little mini wort you are brewing but you have also never let it finish brewing. Just keep it going and going like the Energizer Bunny. The reason I have chosen Nottingham is that it can be fermented as either an Ale Yeast or as a Lager Yeast. Fermentation can be kept at a lower temp so it will not work as fast.
Am I on a good track or am I going to run into mutation in this way. Give me your input.