While Republic Commando never actually got a sequel, for a short time plans were in place to make one. At Lucasarts HQ, there were two competing storylines vying for selection. Brett Douville, lead developer on the game, has been speaking with cinelinx, and says that while both were set in roughly the same time period, they had very different focus:
There were two competing stories that were being pitched, one being developed by Tim Longo and one by lead level designer Kevin Schmitt. In one, you would have played the side story of Revenge of the Sith and carried out Order 66, hunting down Jedi as a team. In the other, Sev would have been the first man in the Rebellion army — the tagline was something like, "Every Rebellion begins with a single soldier."
While the latter might have had a cheery sense of optimism about it, how great would it have been to play the former? Provided, of course, the game made it a little harder to actually kill them.
As for why that sequel never got made, Douville says that just as the storylines were being put together, Lucasarts decided on a company-wide "reboot", and most of the developers of the original game up and left. They hadn't even had a chance to formally pitch the game to executives yet.
A sad tale, then, but if Disney were willing to resurrect Star Wars: Battlefront, then there's hope somewhere down the line that they revisit the idea of a tactical FPS as well.