well... tell me which calls ARE handled by Unity - I assume if you call into Unity directly it answers and you can check your messages and the like, right? So when you call a particular phone extension and it's busy or ring no answer, Unity doesn't pick up, right?
This sounds to me like the phone is not configured to forward calls to voice mail on RNA/Busy conditions - this is a configuration done on the switch itself (not sure which switch you're using here) - typically there's a system wide default for which extension to forward calls to in this scenario and that extension is normally the head of the hunt group the Unity ports are in. If that is not being done then Unity isn't going to pick up - we can't we didn't get the call.
Unity is not going to simply ignore a call forwarded to us and not pick up so I strongly suspect we are not getting the call sent to us in the first place - which means there's nothing you can "fix" on Unity's side of the fence to make this work for you.
Sounds like you need to track down someone that knows something about the phone system you're working with to help out here.
