I found this out the hard way Thursday night:
If you're doing races, your progress will not save until you exit the racing session back to Freemode.
We'd been racing for a couple of hours and got stuck on a loading screen. When I went back to dashboard and reloaded, my character came back minus the 7 levels and $100,000+ in cash I'd made.
So, I'd advise that every 5 levels or so, you back out into Freemode to save your game. If someone hosted the race by going to the race marker, you'll appear next to it upon leaving the race and can just re-start it after everyone's data has been saved properly.
Also, it's not saving other bits of progress, either.
For instance, I've completed the Boneyard Survival three times now, once by myself. I have the achievement and my stats say the highest wave I've reached is 10. But the progress for having done a Survival at all still sits at 0/6. The green checkmark even is removed once I load up the game again.
Also, I keep getting told that people are beating my best lap on Criminal Records with times that are greater than the ones I managed to actually do on the track. I'm told someone beat my time with a 0:34 lap, but I've done laps that have been 0:26 or 0:27 routinely. So it doesn't seem to be saving that data properly either.