What version of RF 4.?.?.
I had the same issue and it went away when I upgraded to RF 4.3.2.Final.
Now I just press the escape key the the suggestion box closes. It working fine now with IE 10, FF 22.0, and Crome 28.0.1500.72.
I upgraded to 4.3.2 and this now works. When I click elsewhere, the drop-down disappears.