I'm not sure this is something that can be explained away through some sort of inventive story explanation that everyone would generally buy.
It's simple enough to argue that Janeway demoted Tuvok as the result of his mutinous activities in "Prime Factors". His "extra" pip disappears after that, and although the disappearance is an odd and protracted affair where the pip flashes on and off between scenes of "Cathexis", we could turn a blind eye to that.
It's not our eyes or our plot-analyzing intelligence that present the problem here. It's our ears. On half a dozen occasions throughout the first season, Tuvok is verbally identified as "Lieutenant", not "Lieutenant Commander". Some of these we might chalk off as Janeway considering Tuvok her trusted lieutenant, regardless of rank. But several are formal introductions, often by Tuvok himself - say, in "Ex Post Facto". The short form "Commander" would be excusable there, but the expression "Lieutenant" would not.
Assuming that Tuvok got demoted presents us with several advantages. Many other characters got demoted around that time, too: B'Elanna Torres had been wearing varying "custom" versions of the Maquis pin, ranging from Ensign to full Lieutenant, but now stabilized on Lt (j.g.), and Tom Paris dropped from full Lieutenant to junior rank. Torres was part of the "Prime Factors" mutiny, and it's easy to believe Paris would find ways to make Janeway sufficiently annoyed at him.
If we assume Janeway demoted Tuvok, then we can argue that Janeway never promoted anybody. She just restored Tuvok's rank later on, much like he restored Paris' after the boy had suffered through his "30 Days" demotion penalty; perhaps she believed that she had no authority to promote anybody without first clearing it with Starfleet. This explains poor Harry Kim, the Eternal Ensign!
Hey, if skippers who are cut off from home base don't get their promotions confirmed, we have a long queue of cases that this could explain. This is why Spock is still a "Lieutenant Commander" in Starfleet's books despite wearing full Commander braid; this is why LaForge didn't get promoted on schedule, as he was stranded on a long and dull deep space assignment aboard the
Victory; etc.
But, as said, this all requires us not to believe our ears. Sure, Trek is a visual type of entertainment first and foremost, but still...
Timo Saloniemi