@siftandwhisk You have stated that if you remove the adds of the network folks then this stops from happening. Then this should certainly be a issue that has arisen due to the ads. It may be js conflict between those of the ads and the navigation that appears in smaller devices. This certainly does not look like a CSS issue. You will have to 1. Not use those ads and try using some other ads 2. Hire a developer to fix this js issue.
I actually just removed the HTML/Javascript adder widgets that contained those ads, saved it, and refreshed the page, and the menu is still disappearing at smaller resolutions. In fact, I went a step further and removed ALL the content from the sidebars, and I still have the same problem. Is this possibly a problem with the responsive design?
My apologies, it occurred to me that perhaps a plugin I had installed was the issue, and after going through each one and activating/deactivating, I discovered that a Social Sharing plugin was causing the menu issue. I uninstalled it, and everything is working normally now. Thanks!