I think I have found a PGR3 bug. It is not easy to reproduce, but it may be useful for you to know before getting quite disappointed, as I did.
After hours of tentatives, I managed to complete a Hot Lap on the Nurburing, that was also the last race to go to complete some tournament in the solo career. Nonetheless, I was also for the first time in League 1, 44th!!! I felt so satisfied and relieved, that I wanted to spend some time replaying my race and saving it. It was then that for some unknown reason I got logged off Live.
PGR3 then took me back to the very first screen ("press start to begin"), and NEVER SAVED the result of my race ! I went back to the career menu, and the race was missing... but the race was there in Gotham TV!
Luckily what I needed to master the Nurburing was consolidated, and I won the race again at the following attempt, but I don't wish you to feel the same frustration and anger.
I think the problem is clear: the result of the race is saved to the gamer profile during the first next "Loading" screen. You can also see for a few second a small "Saving data..." writing or something at the top of the screen. If you do not get to that point, anything could happen to the result of the race you have just completed. If you watch the replay of the race soon after it is finished, and you get logged off, or the Xbox crashes or whatever, the result is lost. Beware!