John,
A further update to our monitor problem:
After posting my last message I noted that when the display/computer goes into screen saver or sleep mode, the screen was blank with the "Check Cable" message scrolling across the screen. Unplugging the Thuderbolt connector at the computer and plugging it in again was the only way to restor the images from the computer.
This morning I replaced the original cable (and VGA connectors) with a cable that was twice the diameter of the original cable. The monitor has worked flawlessly since then at re-start from the sleep state. I conclude that either the replacement cable, connectors or both do a better job conveying the signals between the computer and monitor. It could be that there is some high speed signal the monitor looks for to initiate re-start that is distorted by the original cable.
With either cable the images and text are crisp with no distortion. I see no need to upgrade to a DVI cable and connection between this monitor and the Mac Mini now that the monitor re-start function is working.
-Mike