I don't have this problem and I launch it through Steam. You can add the game in Steam by adding it as a non-Steam Game in the upper menus in Steam.
With that method you get much better controller support.
You just need to find out where the app is placed in the itch.io directories in Windows. I suggest adding a quick link to the itch.io app directory in Windows Explorer.
Because the downside is that every time there is a new update to BBPX you will have to download it manually and re-add the game manually again in Steam.
I have the itch.io launcher app but just use it for updating the apps.
I launch everything through Steam.