If you visit this website: http://demdous.com/examples/html/serendipity/
and resite it to mobile size, then open the menu and dont close it. Now resize to fullscreen and you will see that mobile menu is still there. How to fix that?
Why do you need to ‘fix’ that? Not a single one of your users will ever do that with their browser. 
Hi,
You could hide the menu with a media query for the larger screen sizes.
@media only screen and (min-width: 960px){
.menu-device{display:none!important}
}
It will re-appear when going back smaller again though but the user will then be able to switch it off. That seems to be the way most of those mobile collapsible menus work (e.g. bootstrap for example).
As Ralph said it’s unlikely that a user will open the menu and then widen the browser but I see no harm in making sure the menu is not visible at wider widths:).