That's a weird one, sorry to hear about that. So to confirm, the game can save once, you can load a game but when the game autosaves a second time it errors out with "Couldn't write save game"?
First, are you using the security sandbox in the Itch app? I believe it should work, but it does some pretty funky stuff so it could be related.
Second, does your Windows username have any non-English characters in it? Some other folks have been seeing bugs around that and I haven't got a fix out just yet.