Check In: Tell a Lie, Get a Check (1984)
Poof, no more Kirk.
Possible reasons via http://zvbxrpl.blogspot.com/2008/10/why-steve-kampmann-left-newhart.html
Based on an earlier post about the re-tooling of Newhart into a better show than it promised to be in its first season (in my opinion, anyway), I’ve been asked a couple of times why Steven Kampmann, who played Kirk, was dropped from the show after the second season. I’ve never been completely sure, and still am not, but there are two pieces of information I did turn up. One was an article about Kampmann from Jul 28, 1988 in the Los Angeles Daily News; it was about something else, but he mentioned in it that he was let go from Newhart because “Newhart decided he didn’t like the focus being put on my character.” (The second season of Newhart included a surprising number of episodes built around Kirk: he got married off, apparently in an attempt to make him more likable, and there were episodes about his dating life, proposal, and wedding among others.)
The other is a September 29, 1985 Associated Press article about Peter Scolari, who after being a guest star in season 2 was brought on as a regular in season 3 to replace Kampmann.
The producers decided to make the switch when it became apparent that Kampmann’s character had nowhere to go. The character was supposed to antagonize Newhart, but he had become too strong.
“When you have an obnoxious character you can go one way, as Danny DeVito did on ‘Taxi,’ and become a character you love to hate,” said Scolari. “Or you can have a character who’s obnoxious and doesn’t realize it, as I do with Michael. This year Michael will be a lot more human. It’s to avoid the same trap that Steven fell into, and to keep in step with the rest of the show.”
Taking those things together it seems like the writers thought Kirk was too depressing and unlikable of a character (getting him married was supposed to make him more relatable, but it actually made him worse) and Newhart didn’t think he made a good comic foil.