Calls forwarding to "Not Reachable" number occasionally during the day

We are expereincing messages left on our "Not Reachable" forward number (a third-party VM service) during the business day when plenty of lines are open.  This is as you might imagine annoying and troublesome.  If I turn off the forward, we get calls from customers saying they called in and "it just rang and rang".  Power-cycled the equipment last night and we are still experiencing this.