Okay guys I solved it! Hope it works for you too.
The problem on my side was that my antivirus (Bitdefender) did not give access to Bannerlord to modify "Secured Files". When I first installed Bannerlord, I had given the game the authority to do but it seems one of the updates has changed that (around version e1.1). So yeah, just gave it back the authority to modify files and it starting saving again without issues.
Here are 2 screen shots (i've got a french reskin so I used a google picture to have first in english, second is from mine.)
Here's the place I got the option for the access
And you just turn on these switches!
Hope it helps!
