After a full day and a half looking at this issue and trying anything I could find, I decided to "force the issue".
Open the Device Manager.
Open the Universal Serial Bus controllers.
Delete the Alcor Micro USB 2.0 Card Reader driver.
I scanned for Hardware Changes, and to my surprise the Alcor node did not reappear in the USB controllers list.
So, maybe out of force of habit, I restarted the system.
After the reboot, I opened the Device Manager again, opened the USB Controllers node again, and found that the Alcor was still not there. However, in Disk drives, I found a new node called "Multiple Card Reader USB Device". I plugged in my SD Card and
it came right up! Further tests indicate that the fix is stable and continues to work.
Adding to the mystery, I looked at the event log and while that node had actually existed since the machine's birth (in 2013, as a Win8.0 box), it was mysteriously deleted on November 5, 2014. I upgraded from Win8.0 to Win8.1 on September 9, 2014, so the
deletion did not happen in the Win8.1 upgrade.
FWIW, the machine in question is an HP Pavilion p6-2350, with Quad-core AMD, (only) 8GB RAM, 1TB HDD.