Hm, I tested it in FireFox and the tabs were there the first time, gone the 2nd and 3rd, and there again the 4th. Hmmm. Odd.
The code is the same everytime - I checked. So it isn't a dynamic issue, where there's a code mishap every once and awhile or something.
I've never seen this before, but WordPress is considered one of the best, and if there was an error in their code, they would find out soon enough and fix it. This leads me to believe it isn't on the coding side of things.
The only thing I can think of is the browser having some sort of quirk. Specifically, what's quirking it, I'm not entirely sure. Sorry I wasn't of much help, but I think we've narrowed it down to a browser issue...
Thou com'st in such a questionable shape
Hamlet, Act 1, Scene 4