I have been having this happen. I can't quite put my finger on it, but often I have to go into another time trial and do one lap and back out for it to register (even when I was over by many miles already). It also seems you have to have put up a time for all three tracks.
Lately I have been having this issue where I complete the drive and when I get out of trial it does not give a car and when I check the stats it shows it did not register the miles I just drove. Sometimes it even crashes the game. I have to get to 25 miles, shut down the game and come back in to do the last mile, even then I have to do the extra track after. There may be a connection to track rotation/races going on at that time, but not sure.