One thing to take heed of though, is landscape-portrait-flipping, which happens annoyingly often. In this case the page will redraw. As Rhukster said, you want to make sure that you either eliminate the breakpoint range that causes the floating menu header, or change it to the desired behavior.
In most cases of responsive design, the breakpoints are not static but overlapping ranges. Thus if you remove, say, everything between small phones and extra large desktops, the page will only render in the former if it is a mobile-up design (the breakpoint takes presedence over all other considerations until a different breakpoint matches).
A good example of improper use of these ranges, or they may in fact be static, are some of the modern WordPress sites that feature a static navbar that reduces to hamburger menu. There is a good portion of resolutions in which the same behavior as you describe occurs: Menu floats and crashes with content, where it would be expected to reduce to the menu-icon.
Thus, consider which breakpoint-ranges are defined and how they operate. Chrome's developer console in mobile-mode shows the various ranges, which should give a good indication.