So today I've decided to have a go at this game.

I've completed the cave level, went to the hub, started and finished the first medieval prison level, and went to the hub and quit the game.

The next time I've loaded the game I was at the hub and selected some new upgrades and whatnot. Then I went to the teleport, which I assumed would teleport me to the start of the second medieval level.

But when I loaded it, I was at the start of the first prison medieval level. The one I've already beaten. That doesn't seem right to me.

So what, am I supposed to beat all three levels in one go? Where's the logic in that?

Yes you have to beat a chapter (2-4 levels) before the game will save when you are back in the workshop.

So when a chapter has 4 levels, I also have to beat all four before the game saves? That's quite dumb.

Exactly that. I'm totally fine with that little extra challenge. Getting through a couple levels is not a big deal if you know what you're doing.

Nooooooo.
This is so wrong.

I bought the game, but discovered I had to redo a level if I die.
Now it seems I have to redo the whole chapter?

I don't have the time to do this.
This should reason enough for a refund.