They may not have taken the effort to explain it in-continuity on TOS, but on this type of show, it seems to be pretty standard for most of the actors to get at least a couple of episodes off per season. On TNG, IIRC, everyone but Stewart and Frakes was routinely missing for two or three episodes a season.
...The problem lies in justifying the absence in-universe. Unlike TNG, the plot logic of TOS doesn't provide Scotty with any sort of an "escape pod" by which he could leave the ship for the duration of one episode.
Having Scotty not appear in an episode where the ship isn't facing an engineering crisis and isn't in need of a third-in-command when Kirk and Spock are otherwise engaged would be justifiable. But out of the 78 hours of TOS, it's not easy to find one that meets the criteria!
Certainly "The Alternative Factor" fails in this respect: mere consulting of the ship's dilithium specialist is insufficient for saving the vessel, and Scotty should have been brought in to consider alternatives in case Masters' efforts fail or the crystals can't be recovered from the larcenous Lazari.
...What other Scotty absences were particularly notable? The likes of "Miri" or "Dagger of the Mind", with all the important action taking place off ship, can easily be excused. The likes of "Court Martial", perhaps not so easily. But "The Alternative Factor" still seems to stand out as an engineering-heavy episode without a chief engineer.