What do you mean, it doesn't start the challenge or the times don't get submitted to the leaderboard?
Does it only happen during leaderboard challenges? Can you start a race or practice session with the same car and track? This might be caused by corrupted data, so if you haven't already verify the games cache files in steam. To do this right click the game in steam, select properties, select the local files tab and hit the verify button at the bottom. After that re-boot your system and try again, maybe it helps.