Peter Adamson pointed me to this interesting page, collecting titles of some current and recent doctoral research projects in ancient philosophy in the UK. The first thing to note is, I suppose, the number: more than 50 projects begun since around 2010. I don't think that's too shabby, to be honest, and it suggests that the discipline in general is in a relatively good state.
One point to bear in mind is that this is the list taken from the Institute of Classical Studies so it gives those projects that are in the main being done in Classics Faculties and Departments rather than in Philosophy. So the total number in progress will certainly be higher. And it also might account, I guess, for the fact that if you look down this list you'd be forgiven for thinking that Plato and Aristotle are not all that popular these days. That can't be true, can it? Would the picture be more familiar if we add in those projects being done also, say, in the Oxford Philosophy Faculty or in UCL and KCL Philosophy?