I always called the DH rule the Mickey Mantle rule, allowing the hugely popular Mick to continue playing after he could no longer field. Whether that conjecture is accurate or not, this AL fan (and #7 fan) says it is time for the AL to lose the DH and not the other way around.
Mickey Mantle retired a few years before the DH. Maybe you were thinking of someone else?
Mantle retired five years before the DH was adopted by the American League. The poster boy you want is Tony Oliva who missed most of 1972 after knee surgery but came back and played four years as a DH with the Twins before he retired. He never took the field again once he became a DH.