1. I don't think the fanbase for DS9 is the same as that for TNG. To assume so, just because "Star Trek" is attached to both of them is a fallacy.
TNG, which is I assume what you hold as the benchmark here, is a happy shiny Trek for fans who like short stories about aliens of the week and Our Squeaky Clean, PC-Perfect Heroes running around the universe, helping everyone 'evolve' into something exactly like....well....THEM.
DS9? Ain't that.
The DS9 characters are far too busy trying to survive an intergalactic WAR, burying the dead, and saving the AQ from imminent conquest by a far superior force to worry about helping aliens of the week 'evolve' into a bunch of Federation Mini-Me's.
Thank the Prophets Picard wasn't running the Dominion War, or the entire AQ would have been under the control of the Dominion by the end of DS9. Because Picard would never in a million years have brought the Romulans into the war the way Sisko and Garak did.
No...DS9 was far too upsetting to fans of The Perfect Heroes....because DS9's heroes are far from perfect.

They get their hands dirty - even bloody. They do not live in the utopian world that the TNG crew lives in on board their Ship of Peace, Tranquility, and Most of All, Perfection.
A better benchmark would be to measure DS9 against the performance of B5, which was on at the same time and also featured imperfect heroes and an intergalactic war (really, two) done in an extended arc format.
However, that is neither here nor there. I just don't think TNG and DS9 had the same audience, because they appealed to different sorts of fans. Yes, there was some overlap when it came to a core group of fans who will watch anything with the Star Trek name on it. But as has been evidenced by the ghastly box-office performance of Nemesis, that core fanbase is alot smaller than we like to admit here on a Star Trek message board.
2. I think the long story arcs played a part as well. Fans who were used to tuning in to Trek just when they happened to be at home found TNG easy to follow. But that same demographic would have dropped DS9 because they'd be lost quite quickly with that sort of viewing behavior. Remember, no TiVo or DVRs back then. At the very least, you had to have tapes for the VCR and a more than casual desire to watch the show, or you'd forget to tape it if you weren't going to be home. Not really conducive to the casual, drop-in fan.
3. As has been mentioned about 59,208,992 times in the past 7.5 years I've been moderating this forum, TNG faced virtually no competition when it came on the air - no other scifi shows, and cable as we know it now was in it's infancy.
DS9 had TNG, VOY, and B5 as direct competition for TV-watching hours...and aired during a time when cable was growing at explosive rates, thus creating ratings erosion throughout the industry - not just with regard to DS9.