Menu disappears on smaller monitors

I found that if I shrink my browser window (which has a 1600 pixel width when full), the navigation completely disappears and the “menu” link for mobile devices doesn’t appear until the browser window is the width of a cell phone.

The reason I’m concerned is because I viewed my site on a computer at the library, whose monitors were older and smaller and even though the browser window there was full-screen, the resolution or screen size was small enough that the navigation didn’t show at all there.

Any suggestions on how to fix this?