It seems that one or more of the patches were nonstandard and required a reboot or other interaction. The designation "In Progress" apparently doesn't distinguish between actual processing by "Update Connection" and waiting for SA intervention to reboot the target machine. I discovered this by using "Update Manager" to examine the machine that was permanently indicated by the "Updata Connection" web app to be "In Progress." Update Manager revealed that some of the patches that were in the set of jobs that were "In Progress" required rebooting.
I bounced the box, and then checked "Updata Connection" the next day, and the "In Progress" jobs had cleared.
DG