I honestly have no clue on how to fix that, itch.io kind of does the updating itself, i just give them the newest game file and i use an official program they have to upload it (you are forced to use the program to upload games over 1 gb)
i'm not sure how it works but if the way it works is what gives you problem i cannot do much about it, maybe try uninstalling and reinstalling? if you don't delete cache or anything else it should keep your saves
if you want to be extra safe and you can access the save/load menu in the game, renpy has an option to cloud your saves and then load them in a different device (the upload/download sync button)
you should be able to use that to save your data in a different device while you reinstall
thats the only solution i can think off if updating the game is the thing giving you problems to be honest