I have added an outline of Robert Barham in the Outline section of his profile, taken from http://www.barhamhistory.com/pdf/Barham%20Descent.pdf.
The outline states Robert to be a minor at the time of his father's death (1614). This would make his birth as 1584 unlikely, which would have Robert as a 30 y.o. in 1614. Robert cannot be more than 16 y.o. in 1614, giving his birth no earlier than 1598.
This date gives a more plausible age of Robert on his death in 1683
Managers, please review and make a change in the D.O.B. as appropriate; suggest 'after 1598'