I then dug out a Windows 7 (32-bit) laptop and as soon as I booted it, it started doing all these system updates as I hadn't had it running since last April. It took a while but eventually the Sena software was downloaded and the proper USB driver installed. All this while it was trying to download 50+ software updates and virus signatures. When plugging in the still dead appearing headset, I got the characteristic tone from Windows that a USB device was plugged in and recognized. Started the Sena software and proceeded to ignore all of the warnings that a Sena device was not detected. But when "Update" was selected, it went all the way to completion and near the end of the process, I was prompted to power on the headset. Upon completion, a dialog box suggested that I delete any Bluetooth pairings and recreate them.
After all this, the headset now works again with my iPhone (as a phone) as well as a music player. In the past, I've missed a couple of calls while riding even though the headset was turned on. The media played as well as the intercom but just not the phone part. After the firmware update, all is good once again but I'm not sure that I want to attempt to update the other headset.
BTW, five hours later and Windows is still installing updates.