I am trying to think how his makers know that or even could know that David (and other androids) are immortal. The fact that androids have sort of messy and complex insides suggests to me that they could easily wear out. Is the idea explored? Is it suggested because they can continually repair David that he is effectively immortal or that his mind can be implanted in another body?
When Weyland is, in hologram form, talking to the group on the Prometheus, he says David will never die:
Here David himself says he will not die: Interpretation of the dialog between David and Weyland
I am a little surprised at the downvotes. It is clear that weyland thought david would not die -- he said exactly that. I would like to know why he thought so.