You can fix the disappearing subcats by changing the first 0 to -1px (top margin):
stylesheet.css (line 408)
Code:
#navCatTabsDropdown li ul {
    background-color: #AF5980;
    color: #F6D2E4;
    margin: -1px 0 2px 2px;
    position: absolute;
    visibility: hidden;
    width: 215px;
    z-index: 100;
}
There appears to be a 1px border around the <ul> and when the cursor is moved slowly over it, the border hides the container from the mouse... strange I know, but the negative top margin fixes the flicker.