Well, I figured out what the problem was, but not the cause. I rather belatedly noticed that the time on my receiver was completely wrong! When it was 8:26 PM, it was claiming it was 6:51 PM.
I had this problem happen a few years ago, and I had forgotten about it since then. That time, I think it was off a whole number of hours as if it had the time zone wrong. This time, I have no idea what happened to it.
A reboot fixed it.
How does it set the time anyway? I would presume from the satellite, since there's no guarantee that it'll be connected to the internet. If the dish was blocked when it does the nightly reboot, would it come up with a random time?