A few reasons.
The 1983 game. It's been well-documented.
Location. Cincinnati is inferior in every way to Kentucky. There are more fans in their own city of UK (and maybe UL) than UC. Most non-UK fans in the Tri State area can't stand UK and we would be doing nothing but giving them potential satisfaction and ego by playing them. UK already dominates the region with fans, recruiting and history, there's no reason to play them, especially if they don't provide a legit non-conference game every year (which they don't, at least not better than any other game UK could get).
There are plenty of other regional rivalries that have come and gone. Indiana. Notre Dame. There are others we could start up that could offer as much or more than Cincinnati. Ohio State, Purdue and Illinois come to mind, especially if we aren't playing Indiana anymore.