The way I see it, most of the interesting -- or, at least, layperson-accessible -- philosophical questions in mathematical foundations are either as solved as they will ever be -- e.g., Gentzen's consistency theorem -- or resolved as unsolvable -- e.g., Goedel's incompleteness theorems, Tarski's undefinability theorem.

I see it somewhat differently. I think philosophers were interested in the classic debates between the likes of constructivists, finitists, logicists, formalists, and realists (for lack of a better term), since they all had direct philosophical implications about the metaphysics and epistemology of mathematics. This naturally led to philosophers being interested in formal systems that would lay bare exactly what principles large portions of math could be derived from - e.g., what can be derived from finitistic reasoning (construed a certain way), or constructive reasoning (construed a certain way), or purely logical principles, and so on.

While specific results (like the incompleteness theorems) certainly impacted these debates, I think philosophers' interest in mathematical foundations has died down for other reasons.

One reason is the greater reluctance of philosophers these days to tell practitioners of other fields how to do their business. So there is less support for 'restrictive' philosophical views that say mathematical statements can only be true/meaningful/whatever if, say, they are proven by constructive means, or only use impredicative definitions, and so on. That, of course, doesn't mean that constructive or impredicative mathematics isn't interesting in its own right, but I think there is less interest in those views insofar as they anser metaphysical or epistemological questions.

Another reason goes back to Benacerraf's "What numbers could not be" point; I think most philosophers of math these days agree that there's no sense in debating whether mathematical objects are 'really' sets, or categories, or numbers, or something else. So while philosophers of math still pay attention to set theory, I think it has less to do with thinking that set theory is a 'foundation' for math and more to do with the fact that it happens to be the setting for some philosophically interesting questions (e.g., whether the continuum hypothesis has a truth-value.)