DS9 was so badly treated as a show in its later years. I have always been a trekkie but could never catch it as it switched timeslots every season and I was in elementary/middle school when it aired. I remember catching the series finale one day and going to myself, "Holy crap it's over!" and "Wow, this show must've been awesome with all the parts they are wrapping up."
Sadly reruns did not play things in order so I was never ever able to really catch up with the show.
It was only with Netflix and the release of the DVD's that I was finally able to watch the whole show straight through around 2006 and what a ride it was. The finale had whole new meaning for me as it left a yawning pit in my stomach as I had to said goodbye to the characters I had come to love.
I think the main reason DS9 has so much legs is that it really maximizes television as a format and develops it's characters over its 7 year run. Nog becomes a starfleet officer, the wet-behind-the-ears doctor is not a mature veteran of war, and so on.
Even better are the numerous relationships which we get to see develop over the years. My favorite was the friendship of Garak and Bashir. At first bashir is a naive young doctor that has no idea what to expect of the mysterious Mr. Garak. By the end of the show, Bashir and Garak's friendship is on a whole other level. There were so many characters and so many relationships intertwined with each other that DS9 felt like a living, breathing world with characters I really cared about.
Many trekkies are right that DS9 is not quite Star Trek. It didn'
explore as many grand big-picture sci-fi plots as TNG did; it focused on relationships and characters and was closer to a drama than science fiction; at least by Trek standards.
Many of the things that make DS9 loved by the few who got to see it in its entirety are also those things which hurt it in terms of ratings and popularity. There were no DVD's, no netflix, no online way to catch up if you missed an episode. Nowadays, we kind of expect it in serious dramas. Studio heads are no longer scornful of serialization with true character and plot development; in fact they encourage it because serialized shows have the best DVD sales (For example the CSI shows have great live ratings but mediocre dvd sales). In this way DS9 was ahead of its time.
However, I would have to disagree saying that DS9 is growing in popularity. The show has been off the air for 13 years now and it is no longer seen on US airwaves even on cable. It's a great show and I'm grateful that the star trek name allowed us to get 176 great episodes. Think about it, that's about 9 20-episode seasons today, and about 13 13-episode seasons of a Cable TV show (like mad men).
I think people are appreciating it more now though because sensibilities and expectations about serialization and character development in TV have changed for the better.