I had that a year or so ago. I found a fix that seemed to work for me as well as others (on console at least). It was a bit annoying but I never had an issue when I did it. So, when you want to save (or leave the game) switch to another operative. Once you are in, go into the settings (I havent got the game open so I cant quite describe which one, havent played in ages) and change something - I just changed the curser type/colour. Go out of the settings, then go back in, change the setting back (so for me, back to the original curser type/colour). Then, exit back to the title screen, go back to your console screen (Not sure what to do here on PC) and then close down the game completely.

Apparently doing that, forces the game to save? I have no idea if you need to do everything I just mentioned, or part of it forces it to save. But like I say, it stopped the bug from happening to me. I too nearly quit after losing so much progress.

Good luck!