Not sure exactly when/why Puzzle Place went off the air, but most kids shows are only produced for five years. The reasons are mostly economic.
At the five year mark there are enough episodes for a series to be endlessly repeated daily. The cost of producing shows goes up every year while TV station's budgets for childrens programming doesn't, mostly because pre-school shows like Puzzle PLace are ad-free so they don't generate advertising revenue. This is why most stations have abandon children's programming to PBS and the specialty cable networks (Nick, Noggin, Treehouse, etc.).
When shows do run for 5+ years the reasons are, again, mostly economic. "Sesame Street" and "Barney" are two exceptions because they generate millions in merchandising (Sesame Workshop isn't commercially-oriented, but they rely on merchandising revenue to fund their shows). PBS/YTV's hit "Big Comfy Couch" recently had a 6th season produced for the fall (five years AFTER it was cancelled) because the Canadian producers insisted on producing a new season as a condition of renewing their deal with the show's U.S. distributor, who wants to keep distributing the show in part because they make millions from merchandising.
Guess money makes the (kid's TV) world go `round.
Anyways, once a show is not being produced any more and has been rerun for a couple of years (or less) it is usually pulled to make room for something else.