I think Star Gate's problem was that they came to rely too heavily on the story arcs of the villains they ended up defeating and eliminating, or in the case of SGA, they depended too heavily on just one villain that was never well developed.
The writers basically shrunk their own universe, going from one of amazing potential, variety, and wonder in the early seasons to "Well, we're pretty much done here. Let's wrap this galaxy up."
The premise is still perfectly sound. We have a means of visiting an almost infinite number of planets so we can walk into an incredibly large number of situations, like a more rational version of Doctor Who or Torchwood.
With SGU they found a way to dispense with maintaining so much of the accumulated structure (the political complexities of Washington and the SGC), but also overly limited the show's freedom to just explore new planets by requiring each visit to have a narrow purpose. Then they re-introduced Washington complexities again, recomplicating things.