Do you have the car you want to use set as online (share with friends)? If so, try turning this off and see if you can race it again. Had this with my b-spec driver, so might be the same for cars. Never tried so don't know though.
Could it be that you did something in a public race that caused you to get flagged? Or if the room you tried to enter was full. Or perhaps a connection issue with the room host? I would try other public races and see if I could join any of them.
Edit:
On another note if the race has began you can not enter course.
I've entered the Seasonal events online section twice to get a message, "no seasonal events found".....??
Exit, re-enter and it's all good.....I found that strange...