And speaking of EA Sports, I think that's another reason Sega dropped off after the Genesis. EA moved to Sony, and gave token support to Sega, costing it the sports prestige it once enjoyed.
This quote from the videogamecritic.com Saturn review describes it fairly well:
My personal memories of the Saturn involve my longtime buddy Eric, who opted for a Saturn over the Playstation for Christmas 1995. I had purchased a Playstation in November of that year, and for weeks I tried to convince Eric to go with the Playstation instead. He was convinced however that a Sega system would deliver far better sports titles, which he preferred. Unfortunately his assumption proved incorrect. The early Sega Saturn sports games were fairly awful, and Electronic Arts delayed its Saturn sports titles for months at a time. I still remember Eric calling EA out of desperation to obtain the latest release dates for upcoming games. Years later, Eric relented and bought himself a Playstation. Ironically, he gave me his Saturn, and I've been enjoying it ever since.
And after Saturn, EA famously refused to support Dreamcast until it sold a million consoles... then continued to refuse after it easily passed that sales mark.
I believe it was either Saturn or Dreamcast where EA tried to get another sweetheart deal by demanding to be the exclusive sports licensee, even excluding the Sega Sports line.