I've now read through all 3 of the links provided by captainsticks. The prevailing suggestion is to shut down the system, turn off the power supply (this system is a desktop, so unplugging the battery isn't meaningful) for 5 to 15 minutes (I shut it down for over an hour), and then restart. This did not correct the problem. Another suggestion was to go into the device manager, scroll down to the USB controllers, select to show the USB Root Hubs, right click and select Properties, choose Power Management tab, and uncheck the box for "Allow the computer to turn off the device to save power". I tried this as well with no luck.
Appreciate that I'm not getting a "Device not recognized" or any other error message as mentioned in these posts. The mouse has an illuminated wheel which lights up when it is functioning properly. Each time the system reboots, the light comes on near the end of POST and up until "Windows is Starting" (about 5 seconds. It then goes out while Windows continues to launch. When is connects successfully, the light comes back on right before the user log in screen shows up. When it does not, it flickers faintly for a few seconds and then goes out.