Likely D.
Reelected just in time to be a 2024 running mate?
A good running mate for Biden's VP....he would help in the South and Midwest.....Bel Edwards is too pro-life.
An eventual President Beshear is my dream, and this would be the best route to making that happen, so god I hope it happens.
As for the question at hand... Depends on a lot of variables. I think Beshear is personally popular enough to have a decent chance at surviving, and I think this pandemic WILL be remembered (and Beshear’s role in it largely favorably). Plus I’m not even sure who the KY GOP will nominate. If it ends up being a Bevin-esque far right loon like Savannah Maddox, Beshear has a real shot. (I could see Bevin and his legacy being the equivalent of Sam Brownback.)
Overall I rate it toss-up/tilt D for now, with plenty of room to change in either direction depending on how things go from here and how the political climate changes. Bear in mind though that Steve Beshear didn’t seem to suffer at all from Obama’s unpopularity in 2011. He just won bigger than before. Kentucky has historically been very favorable to Democratic incumbents, and not favorable at all to Republican incumbents. Regardless of the national climate.