My friend and I have also had that problem in our 25% career. Having never explored the issue beyond being forced to quit & restart the game, we found a video of someone experiencing the issue on a stream and noticed that the glitch also removes your hard tyres from your possession, rendering races longer than 50% severely disadvantaged if not impossible.
Our workaround is to just start the race and guess when to pit onto Mediums. Because of this, we also know the glitch also affects the AI; all the drivers will put about 4 times during a 25% race, allowing the human players an easy 1-2 finish.
