So, I made that previous post, checked it out in draft form, including (as always) all links and the embedded video. Everything worked fine. Published the post, went to the blog home page, and for some reason, the video wouldn’t load.
Played around a bit, checked the embed code, went back to the host site, and found a new layout of their clips, including another copy of the preview one I embedded. Suspicious now, I checked the embed code of that one, to find it different from the one I had just used and checked. I edited the post to use that new code, and everything seems to be working now.
So it seems, in the few minutes between proofing my post and publishing it, they changed the layout and video sources on the program site. If they’d delayed just a few more minutes, I likely wouldn’t have known the video went dead after I posted. Timing is everything.