I highly suspect your cookies are not saved properly. When you start up the game, does the game greet you with the image below?
If not, local save data is lost somehow at some point (lamp and clues depend on global save data), which could also be a weird Itch-specific issue. I'm afraid there's a high likelihood it's out of my control, but I'll have a thorough look at it.
Maybe switch browsers or wait until the Armor release if you're willing to give it another attempt.
