I remember after Serena won her first major, she was still winning tournaments but she wouldn't become a true Slam contender again for another two years (until 2001 when she lost to Venus at the U.S. Open). U.S. viewers stayed loyal to the sport perhaps because Venus was winning a lot, then you also had Lindsey Davenport who was also a contender for big titles and on the men's side you started to see the emergence of Andy Roddick but all in all, fans were still following the sport (plenty of men were following Kournikova, for reasons we all can guess).
Back then, CBS, NBC and even ABC (sometimes) was showing tennis. For many years (especially in the 90s), it was possible to see the autumn swing (which was mainly in Europe, in those days) almost every weekend on basic cable! No expensive digital tier! This is what I mean by accessibility of the sport. I hear tennis fans complaining that they subscribe to WTA TV, yet they're still missing matches!
Tennis is the only sport, I truly follow on a consistent basis yet, I sometimes find myself watching NBA finals or even an occasional holiday game between teams(on ABC and ESPN, ESPN3) because it's nice to be able to consistently catch games. Tennis used to be this way but is no longer-- in fact, tennis makes it difficult to find and keep up with the sport. You have to be a dedicated fan to put up with half this nonsense.