First make certain that you have installed the most recent version from amo into Firefox 3.0 or later. The next most likely issue is a general problem with middle-clicking in Firefox. If middle-clicking on a bookmarks menu item does not work properly without Stay-Open Menu installed (It should open the url in a new tab, and close the bookmarks menu.), then the problem is a general one, not related to my extension. In this case, there are several things you can try.
Check to see if it could be a problem with your mouse settings. Look for things related to middle-click. Exact settings and their locations will depend on OS and mouse brand/driver. (Perhaps something like 'Wheel button' may need set to middle-click.) Here are some possible locations to check in Windows XP OS; if you are using another OS, they should be enough to at least give you a clue.
If you still do not get middle-click working in Firefox, I suggest posting a request for help at the Firefox support forum. Alternatively if you are comfortable with using beta software, you might wish to check out Stay-Open Menu 1.4 (still in testing), which gives you the option of enabling it to work with Ctrl-click as well as middle-click.
If middle-clicking does work properly without Stay-Open Menu installed, these instructions are not clear to you, or you have some other problem with Stay-Open Menu, please post to the mozillazine forum (also check there for useful information) or contact me.