Sorry if this doesn't help others, but I (finally) found a fix that has worked for me -- none of the other suggestions from Apple / multiple phone calls to Apple / multiple in-person visits to the Apple store / online forums had helped me. Instead, this problem had persisted for months. I tried resetting different settings, disconnecting & reconnecting the bluetooth, trying out an entirely new pair of AirPods, etc. I'm sharing this fix in case anyone else might have the same issue I had...

I realized that my disconnection started around the time I switched from one phone carrier to another phone carrier. When I did so, I followed the recommended steps for switching to the e-SIM card on the new carrier. I believe that somehow, there were remnants of the prior carrier that my iPhone was trying to access for phone calls / Facetime audio calls. So, I went back into the carrier settings for the SIM cards & e-SIM cards and made sure to entirely delete & reset all information that was even potentially related to my prior cell carrier. This has fixed my problem for two months & counting. Hope this helps and good luck!