I'd recommend NOT having a hidden mix of mechanics with 'saves your progress but only this session' AND 'saves your progress between sessions' without explaining it to the player.
I was pretty far through the wretched rotatey platforms sequence but since each bit was worse than the last I got frustrated and took a break. I knew the game saved progress from previous experience, so I closed the browser tab. Unfortunately, when I came back and 'continue'd, I was back in the carton and seemingly no way to continue from my actual last save point, instead I have to redo all of that. So that's a wrap for me.