I just ran through the game and it didn't stick for me, I'll have to look into the files, sorry that it stuck for you, don't think you are missing much but it's still a shame though. I think the save feature is botched on the browser version sadly.
Same for me. I was playing the game through the itch app, I saved and quit and when I came back later the continue button was no longer greyed out but did nothing. A real shame because I was enjoying it a lot but I don't want to have to repeat myself to get back to where I was.
