Ah, so DS9 fell due to terrible competition?
Fans are always making up silly excuses for Trek's decline on TV. The answer is the same that as for every show that declines: people grew tired of Trek and stopped watching.
I don't care that DS9 wasn't as popular. Many popular things are terrible. What I care about is that it was really good. Best characterization and most consistent writing by far. They made some big mistakes with the show (Pah-Wraiths, Section 31, turning Dukat into a mustache-twirling villain, etc) but delivered a higher ratio of incredible hours of Trek to the small screen than any other series.