Two years. And most of the players don't even like Star Trek.
I originally started as a mini-campaign: a planned 4-6 month story arc that wound up lasting the first year. The characters and the storyline interested them enough that we stuck with it & most really like the game now.
It sounds like these guys aren't really interested. If they are, however, then lay down ground rules. Ours were 1) no freakin' kids! 2) no technobabble beyond what was necessary for the technology. 3) no rewiring the freakin' deflector dish or anything else outside of the general confines of what it does. 4) no time travel.
I then bolstered it by trying to make Starfleet, the UFP, and other organizations function more 'real-world' -- Starfleet is a primarily military organization and I added he bureaucratic nonsense and other elements of idiocy one experiences when one wears boots. The UFP is a socialist or communist government; it has its own little problems, especially since it's not a direct representative government at the Federation level -- I based it off a combination of the proposed EU and the Soviet Union, post-Afghanistan (we were playing post DS9). If the universe feels more real, I think the players that are Trek skeptical are more likely to enjoy it.
My input.
"War is an ugly thing but not the ugliest of things; the decayed and degraded state of moral and patriotic feelings which thinks that nothing is worth war is much worse. A man who has nothing for which he is willing to fight, nothing which is more important than his own personal safety, is a miserable creature and has no chance of being free unless made and kept so by the exertions of better men than himself."
John Stuart Mill