2012 was the last year that Houston, Memphis, SMU, and UCF were in C-USA. Tulane, Tulsa and East Carolina left the year after. You can also throw in the addition of UTSA and North Texas into C-USA in that mix.
My guess is that kids in Houston/Texas stopped seeing Rice/CUSA as a viable alternative for football after we left. In fact, it looks like both the Texas schools that were left behind, UTEP being the other, have struggled with that perception.
Rice should probably just drop down to FCS where they'd have a chance.