This has happened for both a PC player (Moza R3) and Xbox player (Old Logitech G920 I think) in a two player career mode.
Can't speak for the Xbox, but on PC I have on several occasions left the pits and had no force feedback, this seems to always be immediately after making a setup change and saving the setup.
It's like the game reverts to keyboard control after the keyboard is used to type the save name.
Easy enough to fix, just disable force feedback and save the profile, then re-enable it and save again. This seems to work on both Xbox and PC.
Is a bit annoying, apologies if its a known bug!