It's been a while since I've seen it so I may be slightly fuzzy on the details, but the reason he was shuffled out was kind of hilarious. I remember hearing this from someone who was quoting Wil Wheaton. I'll have to find the source.

So TNG is airing and they've got different options for the Chief Engineer character to take over, all depending on public reaction to the character. Argyle is offered up as one option. Letters start coming in saying that Argyle should take over as the Chief Engineer. Problem was that these letters started coming in before the episode where Argyle was featured. Theory was that the actors wife had started a letter writing campaign to try and get Argyle as a main cast member. Argyle was quietly shuffled off after that and not considered as a serious candidate.

Found the source! It's Wil Wheaton himself.

Behind the Scenes Memory: The Chief Engineer of the Week in this episode was Argyle, played by Biff Yeager. I don't know if it's entirely true (and this is recalled over twenty years, through the memory of a 14 year-old) but I remember hearing that Biff was under consideration to become a permanent Chief Engineer, until the producers found out that he (or someone acting on his behalf) had encouraged Trekkies to write letters asking to have him on the ship full time. There's nothing wrong with a letter-writing campaign, but it helps if the letters come in after your episode has aired. Yeah, apparently the letters came in before this show went out, and some Trekkies complained that they were spammed via mail (this was well before e-mail was widely used) and those two factors sent Chief Engineer Argyle -- and Biff -- to the Cornfield.