I was unable to register for the CSR at 3pm central. It shows "Race - The Corporate Sector Run (Completed)" in the mission log, but never registered me for the race. Same with and without plugins, I also tried registering for the one at 3am central and it also did not register me. Also tested taking the mission with different ships.

You registered too early and took the Advertisement mission instead.
The real registration mission appears 15 minutes before the race.