July 2020
I had this issue as well (RA not saving and using Steam). I finally gave up waiting on an update from EA and spent a few hours figuring out. Hoping to save others the frustration and waste of time that I went through, I've been replying to posts with this issue.
I posted the solution here: https://answers.ea.com/t5/Bug-Reports/Progress-is-not-saving/m-p/9355854/highlight/true#M617
Hopefully it works for you guys. At the very least, it is something to try.
Now that I've done my good deed for the year, I'm off to finally play RA properly.