Hm, I don't actually know how web renpy saves files, but I would assume it's something related to cookies or local files.
I know you can import/export saves between the desktop and web versions, if that helps?
If you hold down the Control key to skip and put on easy mode you can get back to wherever you were pretty fast too.
I'll probably add a cheat menu sooner or later to help, but that is gonna be a ways out.