Hello, Barb,
Your suggestion of clearing the registry improved things in that before, unplugging the Surface Connect, turning it around, and plugging it back in didn't use to fix the problem. Now it fixes the problem. The problem was (for me) that both monitors wake properly and display the Surface logo when starting up the PC, but then one monitor loses signal at login (though Windows apparently thinks both monitors are working).
This is not ideal but it's better than having to power cycle the entire dock to get it all working again.
Thanks,
Andrew
UPDATE : It looks like MST/daisy chaining completely solved the issue for me! Thanks anyway (and who knows? clearing the registry may have helped too).