appending to this: for some reason, the save data shown in local storage seems to not be current even just after saving. also seems to only show a certain number of items. i might fiddle with it later unless you have more suggestions
There are only 3 available save slots in the game, so you may only see 3 saves in the folder. I'm not sure why they don't seem to be current, though. How old do the files seem to be compared to when you save? Do you still have the game open when you are looking at the files?
UPDATE: The game has since undergone changes in the way saves work.