Yes, it works fine straight from the website as I did it to double check if that was the issue but still doesn't work?
Does the download eventually fail with an error? Can you post your %APPDATA%/itch/itch.log.txt file somewhere?
No there is never a failed/error its just stuck in limbo as an active download.
Also, which games have you tried downloading with the app so far? Links would be helpful :)
https://badcharger.itch.io/anc...
https://muifwego.itch.io/dont-...
https://commodoreshawn.itch.io...
none of which download