does it vary from show to show?
Yes, it absolutely varies. I've worked on modern shows where every episode's worth of material is put together before we tape with no recycling, and shows where it was deliberately designed to start recycling at some point in the season.
Going back, I've seen some paperwork from Match Game '7x and Super Password. Both shows went into the studio with a pool of games that were considered complete units. In MG's case, they had 8, and more or less played them in order, though you'd see instances of them skipping one. Without comparing specific episodes, I can only imagine they would do that because the answers to one question ended up being similar/leading to what was expected for a question in the skipped game. The show's bible accounts for being able to drop questions on the spot, should that happen. But at least in what I saw, if question A wasn't chosen in game 1, round 2, you wouldn't see it until the next airing week, at a minimum.
Nowadays, I imagine Jeopardy! can go awhile before recycling, because they have so much time, material, etc. But ages ago, scans were posted of the show 1 material from 9/10/84. And season 1 was reportedly like a lot of modern season 1s, in that they had less staff, less time, etc.
Looking at those scans, I can see the unpicked $500 Inventions clue didn't replay in any extant episodes. The $500 Foreign Cuisine clue (A stew of various meats, or an old "Jeopardy" category) played on November 26 as a $300 Trivia clue with one phrase added (...a jar of mixed flower petals, or...). The entirely-unplayed Number, Please category showed up again on October 3. Two clues from the unplayed DJ! category Weights & Measures showed up on October 22. Two of the others showed up in May 1985. The unplayed $800 Notorious clue didn't replay in any extant episodes.
-Jason