OK, I thought it was every time change, but it only autosaves on the night-to-morning transition right now.
Will be changed in next update to autosave on every time change + when quitting the game.
Viewing post in Total Maidness! [v1.01 FINAL] (NSFW 18+) comments
Sorry, I feel like I should've said this in the original post. I'd gone several days into the game on the mobile version and it did not save once. I'm currently almost all the way through the first... Chapter? And still there are no auto saves. Of course, I've started manually saving, so I'll live, but maybe you'd still like to know all the details