Yes, we have added this feature in RecentX 4.0.16. RecentX window will hide automatically when a clipboard item is selected (Copied).
Download the latest update from here : www.conceptworld.com/Recent/Download
Also, make sure that you have not accidentally pinned the window (top left Red Pin button in RecentX window may be down). If pinned then it will stay on top of all other programs. You must unpin so that it auto-hides.