I notice that his face appears on every episode from beginning to end, yet he only appears in only a few in the last 2 seasons. Which ones are he in?

Here's what I came up with

1982-83:
Empty Nest
I'm Not at Liberty
There's no business like no business
All I want for Christmas
Wild Blue Yonder
1983-84:
Where the Guys Are
Welcome Home both parts
Low Notes
Fonzie's Spots

I know there are more!

I really don't know what the reason was for this. My guess is that since Richie and Ralph were gone, there wasn't really much for him to do. In 1980 the show began to take on a new twist, and Potsie was an OLD charachter who had been there since day one. There was a lot of new charachters being introduced. Jenny Picalo, Roger, Eugene Belvin, Melvin Belvin, Bobby, Flip, K.C., Ashley, Heather etc. I think the writers were trying to focus more on the new charachters, and they were trying to phase out Potsie, because his charachter was outdated.