The STARGATE TV franchise gave us 10 years of SG-1, plus additional series in ATLANTIS and SGU. That was a 14-year-run in a single continuity. Granted, STARGATE on TV wasn't exactly the same as STAR TREK, but continuity obviously wasn't the problem there; the newer series simply weren't as good as SG-1, so the stories didn't measure up, and the ratings declined.
SGU was a good show with good writing and acting. It suffered because the `true sg fans` were pissed it didn`t have the camp of the previous 2 series, and subsequently they boycotted it(From top to bottom it had the best acting of all the SG series). The result was a ratings nose dive and cancellation of the series.
Rather than appreciating the show for what it was, and allowing the showrunners to try out a different direction, the fans were ironically the reason why the franchise died, and the idea of the continuation of the franchise through spin offs was not even entertained.
It`d be the same as if everyone boycotting DS9 because it wasn`t trek, and forcing it to be cancelled. And then we wouldn`t have gotten 2 more series, and a few movies of star trek.