Hello again bkabouter,
Excellent isolation steps there! With this, we can confirm that the headset is able to pair with mobile devices and your Mac. One question here, around the time that the headset suddenly stopped pairing, is this when the iPhone was updated to the most recent iOS 9.3.2? I'm curious to see if Plantronics has released any information regarding the compatibility of the latest firmware and iOS 9.3.2.
I might suggest contacting Plantronics for confirmation on that compatibility first. Then, with the troubleshooting completed thus far, we could certainly proceed with an iPhone restore. Ensuring that your phone has a proper backup, is the first order of business:
How to back up your iPhone, iPad, and iPod touch
Testing your iOS device with a clean and fresh copy of the software will give us the most accurate results. This is slightly different than a simple software update. This will remove all content from your phone and replace it with a fresh copy of iOS 9.3.2:
Use iTunes on your Mac or PC to restore your iPhone, iPad, or iPod to factory settings
After the restore is complete, set the iPhone up as a blank device "As New," to test the headset pairing. If all works as expected, you may restore your device from the recently created backup:
Restore your iPhone, iPad, or iPod touch from a backup
Best wishes.