I’m not completely following your process.
What I have done when using the same beer for multiple beers is to use the yeast for the 1st beer. Then save it in a quart mason jar. When you need it again, make a starter 1 week before brewing, pulling 3-4 spoonfuls of yeast out of the jar for the starter.
After 6-7 months, toss the old yeast and save the next batch from the fermenter.
Then common number tossed around is you don’t want to go more then 5-6 generations.
If you made 1 batch of beer a month with the same yeast, you could possibly make ~30 batchs of beer from 1 smack pack/vial of yeast.
If you have concerns opening the mason jar that much, you can save the yeast in a pint mason jar, 4-5 of them. And use 1 jar for each new batch of beer.