A B757-200 Captain reported that the First Officer's oxygen mask was continuously flowing oxygen which the crew could not turn off. It was determined they could not remove the mask. The system had sufficient oxygen; so the flight continued to its destination.

Narrative

First Officer donned oxygen mask [while the] Captain [left the cockpit] to start [the] food warmer and use the lavatory. When I returned to my seat the First Officer informed me that his oxygen mask appeared to be [continuously] flowing oxygen. He made attempt to manipulate the mask to stop the continuous flow of oxygen and was unsuccessful; I then attempted to find a way to stop the flow and was also unsuccessful. We noted at this time that the oxygen pressure indication was 1;250 PSI. We communicated with Dispatch and requested [to speak with] Maintenance. While waiting for Maintenance we computed that we were losing approximately 10 PSI of oxygen pressure every two minutes and twenty seconds. We received an ACARS message that the interconnect/voice communication had dropped and they asked to reconnect. Voice communication with Dispatch and Maintenance re-established we detailed our problems of the flow of oxygen and the approximate rate of loss; we requested that Dispatch compute the minimum required to complete the flight to our original destination; and asked Maintenance if there was a way for us to disconnect the malfunctioning oxygen mask. Both indicated they would get back with us. We showed at this time that our ETA was seventy minutes. While we where waiting for the information [we] requested the First Officer and I discussed the oxygen being discharged into the flight deck; we stopped all unnecessary electrical activity and opened all ventilation air and moved the malfunctioning oxygen mask as far away as possible from objects on a precautionary basis. Dispatch returned with the information that 500 LBS would be the minimum; two crew members only on aircraft; and our fuel burn at 10;000 FT if that became necessary; Maintenance Control determined that there was no way that the crew could remove the mask from the system without tools. We determined that the oxygen mask worked as required while donned; that our oxygen loss rate was approximately 300 PSI per hour and that our oxygen available at destination would be in excess of 700 PSI; we established a continuous challenge and response with Dispatch as a precaution to monitor crew performance and condition; we maintained standard diversion airport awareness and continued to filed destination. We landed at our destination with 900 PSI remaining. Concerns: 1. If the First Officer had not needed to use the mask we may have not discovered the problem until further into the flight. 2. If we had been operating in a portion of the world where no diversion was available we would have been in a depleted oxygen condition in approximately two hours plus or minus. 3. Due to the design of the masks there was no way for the crew in flight to remove the problem from the system; as can be done with the older design oxygen masks.