I don’t think it can’ be anything else based on that message. Have you checked the permissions on the folder and compared them to other plugin folders? Have you spoken to the host?
I’m the host and have control of the permissions. As a test, I opened all permissions to all users and was still unable to get the plugin update working. After setting the permissions back, I uninstalled and re-installed the plugin from the download link and all worked as expected.
There is a new version of Responsive Menu Pro | VestaThemes.com available. View version 3.1.22 details. Automatic update is unavailable for this plugin.