Possibly there is a network issue. The AddOn Manager attempts to connect to our webserver to check if there are updates to the add-ons you have installed. If this fails, normally it will just give an error message but the AddOn Manager will still open. It could perhaps be that in special situations, for instance if there is a firewall blocking the connection or similar, an error occurs in the manager which prevents it from opening.
Another potential issue is if you don't have permissions to manage the VNL installation. Maybe you can try as "Administrator".
What plugin are you looking to install? The AddOn Manager really just copies files to your installation directory so one can always just copy the files by hand.