Sometimes while in the duty, the person that is auto selected as leader will forget to hit the "Look for new member" option once someone leaves. Believe it or not, it's very easy to click that window away and never notice.

If that isn't done, then it doesn't put your party up for selection in the Duty Finder and you'll pretty much be sitting there forever. So long as it says "Looking for members" under the dungeon name in the Duty list, then it's got your dungeon up in the queue looking for someone to join it.

Often times however, friends or FC mates will end up being thrown into another group that may just happen to have the same role missing as your group (hate when this happens as tank) so there isn't much you can do about the situation. xD