Hi,
Thank you for the detailed video.
I’m afraid I might not be able to help with this, as unfortunately this is not caused by the plugin. The menu closes automatically, whenever a menu element is clicked, I guess it is an expected behavior. Instead of trying to resolve this via a custom code, first I recommend checking the menu configuration, if there is any option to change to not the close the menu, unless it looses focus, or the user clicks the menu icon again. That would easily resolve this.
I tried to look into a possible custom script, but I cant seem to find which event triggers the menu closing unfortunately. While it is beyond our support, if you happen to know which event might be triggering that (in programmatical terms), then I might be able to suggest something.