Take all cfg files inside your config folder and move them to another folder. Launch a game and if it runs without issues, you'll know that one of your config files is what causes the trouble.
Thanks for the suggestion, I tried that and no joy. I emptied the cfg folder and launched a game, then paused it, and the same thing happens...it pauses, but goes back to Hyperspin, and I have to alt-tab back to it. Then when I hit P again to un-pause, the same happens and I have to do it all over again.
There are several MAME key presses that don't cause the problem: tab, F2, F3, F11, Esc all work in MAME as they should. P (for pause), and F7 cause the return to Hyperspin.
I tried mapping a different key (b) in MAME for Pause, but that didn't change anything.
As far as I can see, there's no key duplication in the HyperHQ keyboard control mapping.

Maybe it's a Windows 7 thing?