I understood what you said, and, it happens to me, at times, but, my solution is quite simple.
I click "reload", and 95% of the time, it works, immediately. I don't know why this happens, but it does.
However, our understanding was that you wish to have a shortcut to open the Tab Menu, and the importance of that is, obviously, not clear. I don't agree that it is a problem confined to the use of the mouse.
Oh yes, the other 5% which don't respond to the first reload, are in sites which are microsoft-centric that they do not accept anything but IE. I avoid such sites, because they are so backward, but, if I have a problem, it, usually, works with the IE Tab addon.
If I would have to rely on keyboard shortcuts, I would never remember them.
Could you tell us about one of these sites, if login is not required?
UserAgent: Mozilla/5.0 (Windows; U; Windows NT 5.1; en-US; rv:1.9.2) Gecko/20100115 Firefox/3.6