That is a real mystery. I tried it again in Win XP IE6/7 - and both still OK here.
The only way I could see your problem was in the free IE tester you linked to; the IE7 tab showed the fault you described.
On that screen, the disappearing menu could be seen to vanish at the point the mouse leaves one menu item on its way to another (child) item, - but there is no gap whatsoever, so I can't think of a reason why the menu should vanish. Usually, even when there is a gap that causes this to (understandably) happen, if you 'twitch' the mouse/cursor fast enough to bridge the gap, it is will nearly always still be possible to keep the menu open - at least once in a while.
As well as the effect happening at the edge of the menu item, it also (coincidentally?) happens just as the mouse/cursor edges over the flash/swf display you have just under the menu.
If you have the site still in Dreamweaver, could you try duplicating the page, and upload the duplicate page without the flash swf on the page? I would like to rule out that coincidental connection.
If the menu now works OK in IE7 XPsp2, try changing the wmode parameters in the flash code (x2) from 'opaque' to 'transparent'.
As you can guess, I'm just fishing in the dark here - but am a bit intrigued to find out what the problem is!