Depends on the show and the producers.
Directors are basically free-lance professionals. They normally come in a week or so before a show films to orient themselves and move on to their next job when filming is done. A lot of producers like this, because it brings an element of variety to their shows while remaining within their formats.
Sometimes it works, sometimes it doesn’t. F’rinstance, a director might not grasp the concept of the show, be able to keep up with the shooting schedule, or get along with the cast. When this happens, he (or she) is usually not invited back.
When things go well, a director can be invited back multiple times. Many episodes of the original ***Star Trek ***for example were directed by two men, Marc Daniels and Joe Pevney. They definitely left their mark on the series.
In some cases, this becomes what is essentially a permanent assignment. F’rinstance, all of the episodes of Barney Miller I’ve seen were directed by Noam Pitlik.
Once producers find a director they like working with, they can come back again and again. Some producers like to direct episodes of their series themselves, like Larry David did with Seinfeld.
On a long-running series, some of the actors with directoral aspirations are allowed to helm an episode; often, they’re encouraged to. Mike Farrell, for example, got his big break while MASH*** was being filmed. So did Jonathan Frakes of ST: TNG. Sometimes these people give up acting altogether and become full-time directors instead, like Jerry Paris (from The Untouchables and The Dick van Dyke Show). The abovementioned Noam Pitlik went from acting to directing as well.
So, who directs a show and how many times he (or she) does it depends on a number of factors.