Thank you! It's really nice to hear that.
I admit, I don't know. The skipping option is a standard feature of the engine we use, Ren'Py. It wasn't something we added, so I don't know exactly how it works. Maybe try deleting those not-properly-working saves (hovering the slot and hitting the delete key) and creating new ones?
Also, sometimes there are repetitious scenes that seem like something you've already gotten and should be able to skip through, but they are slightly different and so can't be skipped. There's nothing that can be done about that one, I'm afraid.
Good luck and I'm sorry for the inconvenience!