The game auto saves on every rebirth and a few patches ago it started saving every 5min. Sorry for the lost days. The game also has offline progress now, which should help going forward.
You can also save by going to the Menu Options (top left) and then the Save Menu.
Confirming this, as of December 2022. Played ~4 hours, incrementing stopped, prestiged, F5ed... and the game restarted from scratch. Firefox, logged into itch, no cookie-denial or incognito mode or any of the like (other itch games w/ autosaves are running properly in the same settings)
