Hi @Stina and hi @DFink, ok, I figured out what the issue is. It is not so readily apparent, so I will explain. I will use @Stina website, since that was the one I was checking, but @DFink, if you need me to look at your site also, I can do that, if the answer below does not help you too.
The first thing you need to do, is to get into the editing mode of the LeftNav menu, which is stored as a symbol in your site. You can access the editing mode of the symbol by double clicking the symbol.
Next, select the element MenuButtonBlock (which is the click region for the navbar). Click on the settings icon so you can view the menu settings:
Next click "Open Menu"
Now that the menu is Open, we want to update the style setting of the MenuButtonBlock, so while the menu is OPEN from the step you just performed, click on the style icon. The current setting for the MenuButtonBlock when it is in the Open state is position-relative, top-left corner and z-index is set to Auto. You need to change the setting for z-index to some number value greater than the the z-index for the left nav panel that slides out... otherwise, the click region on the menu hamburger is not accessible for the second click.
In my test, I just changed the z-index to the open state of the MenuButtonBlock to 999 and then saved change and the menu will work, both open and close.. try that out... here is my screen shot of the MenuButtonBlock style settings:
Let me know if that works for you... I hope that helps and happy webflowing !