Callers cannot hear us

Whether we call someone on our land line or they call us, at some point they cannot hear us at all.  We can hear them saying 'hello? hello? hello?' then hanging up.  We call them back or they call us back and after explaining what has happened, the phone seems to work fine.  Every now and then it would happen again.  So, we bought another cordless phone system.  It kept happening.  Called Cox and tech said the phone line was fine and everything tested great... on their end.  Little frustrated now.