We have a client that experiences the following, but only when Progressive Insurance calls them.
They will take a call from Progressive and park that call. Then, when a person picks up the parked call (hitting BLF of the parking slot), the call will drop. This only happens when it is progressive calling, all other parties park and pickup works fine.
Sounds like it is very consistent, which makes capturing a log all the easier. Whenever you are having an experience that deviates from the normal, this is a good place to start to understand what is happening.