Hmm.. to be honest your problem absolutely has me lost..
The H2 Tag is just simply a heading tag so I dont see how that would affect it (that being said I called it a dozen different names for testing (some not even the word menu) and still didnt make a difference.)
what I did notice Is If I had it calling a Menu that did not exist (For example I only have Menu one created but trying to call Menu 2) it would just repeat Menu 1, But would not display properly (Styles were not being applied properly.)
But if I made it call menu 2 after I created it then it worked just fine.
so where yours is listing but not linking... i honestly have no Idea, only thing that I can think is that a corrupt file somewhere possibly.
I've included an image to clarify what I mean by a second menu. I am sorry that I am not able to be much help... But to be honest I am out of idea's at this point since I dont seem to be able to replicate your problem.
Only thing I can think of is trying reloading your account and re-install the template and see if that fix's it.
Other then that, Thats all I got. best of Luck.