Help, calls at our office are dropping intermittently!?

I'm at the end of my rope! At our office, I somehow got stuck with being in charge of the phones. Well, we have an Avaya PBX, not VOIP, and we are having problems with dropped calls. The phone company and the company in charge of the PBX are pointing fingers at each other. Whose fault is it? Two details: we have two T1s, one for local, one for long distance, all the dropped calls have come from outbound calls to long distance numbers. Also, one dropped call involved someone here calling two people to start a conference call, and during the call, one of the parties dropped, but the other stayed on, thought that was unusual. Whose fault do you think it is? I don't know what to do!