I've battled the same problem, since the last saved date, 16th March.
April was a little different. For some obscure reason, the only saved date was 16th - and I thought finally the problem was solved. But no. Then I got to 28th April, and it saved, as it did the 29th April. Every time I closed the app or my laptop spontaneously rebooted, those were the only 2 saved dates - every other date reset to '0/3', although the 'Done' button appeared on 30th April after I played all 3 games. Replayed every single 'unplayed' game, which was the point at which, after closing the app, I could actually progress to May. Played yesterday, only the Irregular game remained saved. Played them again, played all 3 games today, only the Irregular game played yesterday remained saved. I've had more than one request to make sure I have the latest version of the game, but reading other players' comments that doesn't seem to make any difference. Have had 2 requests to access my Local State and Temp Files, but following the directions to the letter, those are not options that appear - instead I get a single page to "Read and Consent to data usage by "Manuals Library Search" addon", which I'm somewhat reluctant to do, for one thing because it's not what the directions tell me to see.
I found that the puzzles of the last couple of days are now saving but after playing all of the unsaved puzzles, completing them, closing the app, and re-opening it... almost all progress from 13-16, and 18,19 of March disappeared.
