I can't say for sure Randy, unless I could see the counter bore in the valve for the fitting, and the seal area on the fitting behind the hex. But when you say it looks like it should take a square cut or D style o ring leads me to believe it may need what they call a dowty seal washer. It is a super heavy square cut washer with a bonded lip seal on the id of the washer.
Edit: Especially when I see the circular counter bore on the valve. So if it is tapered cut behind that for a round oring than all you need is a back up washer on the fitting behind the hex. Those normally don't fall off as they are almost spun on by hand over the fitting threads.