Okay so upon looking further the exact error is an API (400)
Viewing post in Game I purchased not opening
Of course I can not know what api that is, as you give not exactly much information, but there is html error message 400, bad request. Wich could very well indicate that the game tries to contact a web server and something goes wrong.
As would be consistent with the error the game gives you, it can't confirm your purchase. Itch does not support drm to my knowledge. Not directly at least. But there are some apis apps can use to do that and this involves contacting web servers.
Since I have yet to see a game that does things like that, I can tell you not much beside that something like that exists.
Bottom line is, try to seek out help from the developer. If this is not possible, contact support on itch.
If you go on the game page, in the information section, there should be written a date about last update. This would not be coincidentally be around the time the app stopped working? ;-)