The numbers I have heard in the pro brewing world is about 2 weeks in a refrigerated environment. I am sure others who re-pitch yeast will also weigh in on this with information that may be more accurate. I don’t brew enough to save yeast. However, when I started homebrewing 20+ years ago I saved some for a couple months. It smelled horrible and I had to throw it out.
Jeffy is correct. KISS stands for “Keep It Simple, Stupid.” Kelly Johnson, the head of Lockheed’s Skunk Works, used to use it all of the time to prevent his engineers from overthinking things. The KISS principle has become ingrained in the American engineering community. The first thing I used to do when I received a fresh-out computer engineer or computer scientist was to drive this principle home. Keeping things simple results in a more verifiable product that has a lower defect rate.
Bel Air Brewing stores harvested yeast up to 3 months. Never had it go bad, or develop any “off aromas”. It is stored in sanitized glass jugs, and kept at 34-36 F.
If you do choose to save yeast in the future, one thing that you really shouldn’t do is what homebrewers call “yeast washing” but really isn’t. Don’t rinse it, don’t dilute it with water. Just save the yeast under beer or some of the fermented starter liquid in the fridge.