As previously mentioned by Secret_Tunnel, the cause could be an issue with the itch.io servers.
Tested it right now as of writing this message. No issues.
It would be very helpful if you could tell me what system and browser you are using. Do you get the download pop-up window once you've pressed the download button?
Since the problem doesn't appear for everyone, and since the issue doesn't seem to be on the part of the game, looking for patterns among those who get this issue and directing that information to itch support is really all I can do at this point.