Thanks for such a well-informed perspective. I did see in the research for this that Classics departments are dying out.
But I wonder if that isn't partly an issue of--oh, vile word in this context!--"branding" and if steps like those your college took (in changing the name to Ancient Mediterranean Studies) might be what's needed. As a major, philosophy seems to be doing better than expected (on the evidence of a short Medium piece I did a while back). Then there's all the interest in Stoicism that you see elsewhere.
Perhaps it's wishful thinking on my part, but I can see how--over time--an interest in ancient Greek and Roman philosophy and literature could lead people to want to read them in the original languages. In the meantime, I'm glad you're teaching it and hope your students appreciate it.