Have you verified that you are receiving the CPC disconnect?
I don't know how you can "conference" in on an active line unless your referring to "executive override"
Either way, do that again and then open the line to see if the calling party never hung up.
If it drops as soon as you open the line then you know your system's OK.
It may be a machine of some sort that stays active as long as it hears voice.
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MrG