Hey Clément,
It’s technically impossible to lose experience points. About reputation points:
Reputation is how well you perform relative to expectations in the races you take part in. It starts for all managers at 5000 and increases or decreases based on your results. Similarly to level XP, it will increase by greater amounts if you are racing with managers with higher reputation levels than you.
Reputation is calculated entirely on the level of competition. Seeking out reputable rivals and populated leagues is very important to keep making progress with your own reputation level.
Not doing so can result in decreases in reputation even with good results. For example, let's say a top manager from the Hall of Fame whose reputation is 9000 goes and starts racing with total newcomer managers with 5000 reputation. It's so uncompetitive that simply participating in such an environment can be damaging to a reputation. So, a highly ranked manager could lose reputation even for victories there.
Another example would be if there are only two teams in a league. Whoever wins those races will also surely see a decline in reputation, again because they are not racing in a competitive environment.
The easiest way to keep your reputation on an upward momentum is to keep seeking out tough competition and challenging yourself. By racing stronger competitors, even a poor finishing position can result in reputation gains, because you won't be expected to win. Any competitive results in such an environment will also bring a huge boost to your reputation.