Godzilla is sort of on the borderline between having deliberate "rests" and simply stopping due to falling profits. The original film series went dormant in the mid-'70s due to box-office failure, then was revived for the 30th anniversary, but it was another six years or thereabouts before that revived series continued, due to studio money problems. They kept going long enough to finish with a 40th-anniversary film in 1994, and then deliberately went on hiatus with the intention of passing the torch to TriStar to make an American trilogy and then finally restarting their own series once the 50th came around. But the American film didn't do well enough to get sequels, so Toho rushed back into the game in time for the 45th anniversary in 1999; but as with the original series, the later films didn't do well at the box office and they were losing money by 2003, so they decided to end the series with one more film for the 50th anniversary. I think I may have read that Toho's hope was to resume the series on the 60th, but instead it'll be Edwards's movie that commemorates that milestone.