Roman,

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ITEM1: Desktop Browsers: IE 11 and Firefox 25
Browsers at full width…
Scrolling down the page to trigger the Sticky Header…
The standard logo moves to the top (minimized) and the back ground is a 90% white…
The menu is right below, also with a white back ground…
Then the menu losses the white back ground… the white back ground pulls up… and the menu becomes hard to read as it blends in with the body.
The menu then wraps to two lines.

Update:
ITEM1 RESOLVED: Solution Unknown
Regarding above, today IE and Firefox… without changes, the menu appears to be working okay with normal usage (no reduced width on the browser window). Maybe it was something cached :: shrug ::

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ITEM 2: RESOLVED
Regarding the Sprint Galaxy S3 with FF browser:
The FF browser now allows the menu to be continuously displayed while scrolling down the entire page (beyond the bottom of the menu).

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ITEM 3: DEGRADED
Just for the heck of it… I also tested on the Samsung (Android) Tab and Note 10.1 tablets.
Both tablets are fine in landscape; however, rotating both devices to portrait orientation makes it 95% down the menu and then the menu disappears. Scrolling back up a little returns the menu view. Scrolling back down, again removes the menu. (repeatable)

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ITEM 4: DEGRADED
Reproducing with a desktop browser:
I’m not sure why someone would do this, but…
Win7 IE desktop browser with the window width of the browser reduced to the point the compressed menu icon appears. As soon as the Sticky Header appears the Menu Icon (compressed) disappears and also with the entire Menu (expanded).
NOTE: Might not even be an issue… more of a FYI.

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DIFFERENT TOPIC:
I have found what looks like a Site Name/Title issue duplicating on pages; concern is regarding SEO… do you want that posted into a different thread?

Chad