He lost his place as the regular centre back in 1975 when we bought Dave Watson, with Watson and Doyle being the preferred pairing for the next couple of seasons.
The BM history site players section lists his appearance numbers per season from then onwards (you can access them here:
http://www.bluemoon-mcfc.co.uk/History/Players/Player.aspx?id=548 - they cover all competitions and include both starts and coming on as sub) as:
1975/6 - 35 games (he got a run in midfield when Bell got injured)
1976/7 - 17 games (mainly covering for Watson and Doyle when injured, IIRC - Doyle got a bad one about 2 months before the end of the season)
1977/8 - 49 games (he was pretty much an automatic choice as Watson's partner, overtaking Doyle in the pecking order)
1978/9 - 31 games (we bought Futcher to partner Watson, but it wasn't a successful signing and the new boy only played 21 games, with Booth being preferred more often than not)
1979/80 - 26 games (Caton was an ever-present that season, while Booth competed with Futcher and Stepanovich to partner the youngster)
1980/81 - 37 games (got a decent amount of match time, but Caton and Reid was generally the first-choice pair including in the Cup final)
He played a single game at the start of the following season but was basically surplus to requirements after John Bond signed Kevin Bond so was sold to Preston early in the campaign for a pretty small fee.
I was only a kid, but I think that Watson was, probably fairly, regarded as an upgrade and the feeling was that Doyle complemented Watson a bit better. When Doyle left, we'd have been better in retrospect keeping faith with Booth rather than buying Futcher for what at the time was a very big fee, but I think that it was considered that his style was likely also to fit better with Watson's. Moreover, as a star of the England under-21s at the time, Futcher was expected to be a mainstay of our team for a long time to come whereas Booth was already 30-ish by then.
In the days before the concept of squad rotation was really commonplace, Booth was an excellent squad player, though. Even though he was only an automatic pick for one (1977/8) of his last six full seasons at City, he played in well over half the games in four of the other five of those seasons. I have a vague memory of Tony Book commenting that he was contacted regularly by other First Division teams keen to sign Tommy, but the player was happy to stay with City. That was certainly to our benefit.