I have not found any persuasive rebuttals of Popper's argument. If you have found one that has convinced you, I am interested to know it.

Thanks for the question. 

In the paper "A proof of the impossibility of inductive probability." by Popper and Miller, they demonstrated that the truth of a theory cannot be supported by observation. 
The knowledge in AI models is created through a kind of induction (the knowledge is a generalization of observations). AI models lack discrete theory statements, as in Bayesian reasoning and in the Popper/Miller critique; the knowledge structure is continuous. 

Therefore, your comment does not point to a contradiction. It does, however, point to the problem I am trying to express: that modern AI methods cannot produce a coherent deductive knowledge structure. I try to communicate an alternate method.