"Updating FreeBSD repository catalogue" is slow and frequent

[Alan Somers]

On some systems, every time I try to install a package pkg(8) spends five
minutes at "Updating FreeBSD repository catalogue...".  This sounds like
the kind of thing that ought to happen infrequently, say once per week.
But instead it happens on every single invocation.  I've seen it on TrueOS
Edge, 11.0-RELEASE, and 11.1-RELEASE, but not every system.  Does anybody
know what's going on?
-Alan