I can't believe I never noticed this, until this re-read! Archie's initial poking has produced movement from Wolfe, who (we are about to find out) has made the connection between Chapin and Hibbard, the guy who asked Wolfe for help while Archie was away. And this happens:

Wolfe said, "Archie. One would know everything in the world there is to know, if one waited long enough. The one fault in the passivity of Buddha as a technique for the acquisition of knowledge and wisdom is the miserably brief span of human life. [...]"

"Yes, sir. You mean, we just go on sitting here and we learn a lot."

"Not a lot. But more, a little more each century."

"You maybe. Not me. If I sit here about two more days I'll be so damn goofy I won't know anything."

Wolfe's eyes flickered faintly.

...then Wolfe needles Archie, who tells him to go to Hell, and Wolfe replies, Awesome, you're annoyed and therefore awake, let's get to work. (As if it's his job to nudge Archie into activity!)

Looking at it fannishly, I love to envision this as Wolfe's first foray into broaching the topic of not-aging and how useful it would be. But Archie not only takes it lightly but also complains about the very idea, that it would be against his nature and drive him insane, so Wolfe veers away with the typical tactic of snark/countersnark.

And of course we know Archie doesn't seem to stop aging until later in the books. So perhaps Wolfe regroups from this casual attempt, and returns to the topic when he feels Archie will be more receptive?