[I]t was recognized that there was a connection between Nestorian christology and a view of the Eucharist that stressed its memorial aspect rather than the real presence. [p. 61]In context he's saying that this was recognized in the sixth century. If I understand things rightly, it seems that because of the Nestorian objection to the communication of properties (whereby we may say, for example, that God was crucified for us because Jesus Christ is God Incarnate - though of course it must be understood that in his divinity he neither died nor suffered) it's impossible for Christ's Body to have such properties as would allow it to be literally present in the Eucharist - which can only have the consequence of reducing the Sacrament to a memorial.
It's interesting (and unlikely to be merely coincidental) that many Protestants today view the Eucharist as nothing more than a memorial, given that they are sometimes charged with holding to a Nestorian christology due to their unwillingness to ascribe the title of Theotokos to the Blessed Virgin. One must wonder whether that which walks and quacks like a duck is really a duck or not.