Mac OS: Bluetooth headphones lose sound but not connection
This is not necessarily a macOS or Apple problem.  My thought is that you have an issue with the Bluetooth device itself.  

The BT device being connected isn’t a big factor here (well, you obviously need to be connected to transmit data, but that’s not what I’m referring to, here).  The radio signals BT uses isn’t that much different than two way radios used way back when (think of CB radios back in the day)...


Theres a frequency the two devices negotiate to communicate on (breaker one-nine, breaker one-nine)
There’s a broadcast, a handshake and an acknowledgement to communicate (got your ears on, good buddy?  I’m broadcasting in the clear, come on back!)
Then there’s is an exchange of data (there’s a Smokey on your six, be careful.  I’m looking for some go-go juice and to put some groceries down my neck)


In a BT audio device, there’s a DAC, or digital audio converter that translates the digital data to audio.  Think of it as a translator sitting next to converting CB lingo to normal speech (Smokey = police; go-go juice = fuel; groceries down neck = food)

What I believe is happening is this DAC portion of your BT device is crashing.  The connection is still there, but there’s nothing to translate digital to analog and then amplify it so you can hear.  

We can confirm this because nothing you do to the Mac has any effect, however, if you restart the BT device, it works again.  You need to replace the BT device with a new one.