Hi, thanks for playing!
There's a save system if you quit, but losing set you back to square 1 purposefully. This game isn't about catching 'em all in one run, as there are only 10 spaces to store the Automons; It's more of a drafting game than a collecting one. The Autodox does save between runs though, so that's the incentive to replay and win with different combinations.
I had no idea about the itch app thing, I'll look into it