Goto OPTIONS > GAME and where it lists the options for Multiplayer and Singleplayer replay saves, set them to [Enabled - Manual Save].
It should work all the time in Multiplayer,
however in Singleplayer it only works certain times.
The reason you get this message is probably because you started a race/practice, but then pit in/out a few times. Doing that will cause the replay to suddenly not 'record' for some reason
If you want to get a full replay of your singleplayer driving, make sure you RESTART the race in between replays.