The fact that it was a spin-off was also a factor.
As much as some spin-offs become more popular than the parent shows, or "as" popular, a greater number either under-achieve or crash-and-burn. Viewers do find them wearing, if they don't set out a compelling identity of their own quickly. DS9 certainly did that, but (arguably) took too long to nail that down. By the second or third season they were really cooking with gas, but that may have been too late for some.
Deep Space Nine also had a few hang-ups from the start that some viewers may have found hard to take. Being set in a stationary place gave viewers the feeling of a place where nothing much happens (maybe they should've had the Defiant from the start), and the pre-production buzz talked extensively about it being a 'darker and grittier' Star Trek, which may also have turned some away. It was also the first Star Trek to be made by anybody other than Roddenberry (the TOS-movies notwithstanding, but then they used characters and concepts that Roddenberry had created), so in some ways there was the sense of 'other interests' making their own Star Trek out of whole cloth.
I've often thought Mad Magazine gets things quite right in their parodies, usually made very early in a show's run but in retrospect their analysis proves prophetic. In TNG they made a lot of it's lack of drama among the main cast, with DS9 much was made of the tedium of being on a space station rather than aboard a starship. That was a kind of the 'finger on the pulse' about what the wider viewers at home might have been feeling about DS9 in those early years before it "got better".
The addition of the Defiant immeasurably gave the show more scope (without losing it's core style), and "Way of the Warrior" feels in so many ways like an attempt to redefine the series, almost like a second 'pilot episode' for a whole new phase. Even those of us who love Deep Space Nine would acknowledge there's a night-and-day feeling between the first three seasons the the last four, and it extends way beyond simply adding Worf to the cast. The types of stories they could tell changed.
That said, I believe "Emissary" was a ratings hit straight out of the gate. So if viewership went down, then there may be other reasons.....