After reading the actual text of the conference by Kenneth Mackenzie Clark (linked to in a comment below), it turns out that the author doesn't discuss writers in general, but specifically poets, and that he thinks poets stop writing poetry (or, sometimes, good poetry) in old age because poetry requires "fire", which doesn't burn as bright then.

I'm not sure where the OP got the idea of "writers less likely to carry on" but it's not in the text of the conference.