Air carrier flight crew reported duct leak in the bleed air system was detected before pushback. Flight crew refused the aircraft.

Narrative

Preflight planning and preflight activities all proceeded normally for this flight. We were parked at the hardstand ; only accessible by bus from the main terminal. At approximately 45 minutes prior to scheduled push time I observed a BODY DUCT LEAK EICAS message. We also observed a Center DUCT LEAK indication on the Bleed Air System panel. I opened the flight manual QRH and ran the checklist for this EICAS message. The checklist had us close the C ISLN (Center Isolation) switch and the APU BLEED AIR switch. The DUCT LEAK light remained illuminated so the checklist led us to turn off the L or R ENG BLEED AIR switches and the PACK control selectors. Following this checklist we entered the EICAS message in the ELB (Electronic Log Book) and followed up with station personnel to send a Mechanic . We advised station personnel to attach ground conditioned air for cabin cooling. The ambient air temperature was 34 C (93 F). With APU cooling; the cabin temperature had been in the mid 70s; but it began to rise; despite having ground air hooked up.It took approximately 10 minutes for a contract Mechanic to arrive. When he did; we described the problem; and he began looking at the problem and troubleshooting. It only took him a few minutes in the avionics compartment to come upstairs and tell us that he thought it was a temperature sensor issue. We weren't sure how he could have addressed that issue so quickly. We asked him which sensor. He said there were multiple sensors on the entire center duct and he wasn't sure which specific sensor it was. We asked him where those sensors were located. He said they ran the entire length of the duct. We asked if he had opened any panels to check ductwork. He said he had not. He said he cleared the fault and said he thought we were OK to continue.We discussed his actions; threats and possible outcomes; and decided at that time; we were OK to continue. At this point we were close to push time; so I coordinated with apron for our euro control slot time to remain open. Apron advised that we had a TOBT (Target Off-Block Time) of XA19 ; approximately 20 minutes from then. We advised ATC that we could make that time. When the Maintenance Release was released to us at approximately XA10; we called apron fully ready for push and were then told we would have to hold our push; hold position and wait approximately an hour and 20 minutes until XB30 based on a new wheels up time from control. We were told there was a possibility of improvement so we monitored the frequency. Approximately 15 minutes later; the BODY DUCT LEAK EICAS message and Center DUCT LEAK indications both reasserted.At this point; I was not confident that it was just a sensor issue. I was concerned about an actual bleed air leak somewhere in the system. As a part of my flying background in large transport military aircraft ; an uncontrolled bleed air leak and associated fire in flight had nearly caused a hull loss and loss of life during my time in that flying community. That leak has started as a small leak; but had grown over the course of the flight until it reached the point where an immediate divert was the only action that saved the aircraft. This information and the threat of an inflight fire over the ocean played into my decision-making process as all of the events were unfolding.We ran the BODY DUCT LEAK checklist again; as we had previously; put a new write up in the ELB; and asked station personal again to hook up ground conditioned air. We again called for a mechanic . The cabin temperature at this point was in the high 70s; and despite having ground conditioned air hooked up; it rose to the low 90s in only approximately 15 minutes. The cabin and cockpit temperature remained in the low 90s for the remainder of our time on the aircraft while we attempted to determine the extent of the potential bleed air leak. This extremely high cabin temperature was a factor in my thought process; as the flight attendants several times came into the cockpit; telling us about elderly passengers and young babies who were near passing out; having panic attacks; and were visibly upset. Several passengers said they wanted to get off the airplane. The relief pilot spent some his time interfacing with the flight attendants and passengers while the event was going on.The Captain began a series of several conversations with Maintenance Control; dispatch; and with the local mechanic about how we could resolve this issue. These conversations would last for approximately an hour and a half. Maintenance Control advocated for securing the APU bleed air valve. We were not comfortable with this; as our schematics in the Flight Manual showed that a significant portion of the demand items on the center duct would still be exposed to high temperature bleed air from the engines even with the APU Bleed valve closed. The Mechanic on the ground with us described this also; based on the duct leak sensors and where they were located. Maintenance Control at one point talked about a check valve; which would prevent bleed air from flowing through part of the center air duct. The check valve though; is clearly shown in the schematic; and all of the demand items previously described are upstream of that check valve; and would be exposed to hot high-pressure bleed air from the engines during operation with the APU bleed air valve MEL closed.We considered the possibility of closing the ISLN switch; but that would remove the air demand pump; cargo and bulk heating; and hydraulic reservoir pressurization for the center system. We were not comfortable with this either. Maintenance Control at no point advocated closing or applying an MEL to the C ISLN switch. It was a discussion point in the cockpit though; because the checklist would have us close the C ISLN switch if the indication reasserted in flight.Further; if the BODY DUCT LEAK EICAS message reasserted in flight; and the checklist proceeded the same way it had on the ground; we would be looking at partial or no pressurization; and potentially an emergency descent to bring the cabin altitude to a safe altitude before diverting. This possibility factored into my thought process and decision making as well.In short; we were receiving conflicting information from the local Mechanic our flight manual; and Maintenance Control. The flight manual clearly indicated that hot high pressure bleed air would be flowing in part of the center bleed air duct even with the APU Bleed valve MEL closed. The possibility of an uncontrolled bleed air leak and subsequent fire associated with the uncontrolled bleed air leak was a risk that I didn't believe we should accept. As our flight involved an ocean crossing; there would be hours when we would have no divert field available. If we were to encounter a fire associated with bleed air in that scenario; the consequences would likely be catastrophic.After approximately an hour and a half of troubleshooting and discussing; reading the flight manual; and looking at options; I believed that taking that aircraft across the ocean with a potential bleed air leak; even with the APU valve secured closed was an unsafe decision. We believed that the ductwork should be inspected for leaks; particularly a small leak; which could be indicative of the leak indications that might take the amount of time these had taken to assert on the EICAS. While all of this was going on; there was a growing time pressure to make a decision based on unhealthy and unsafe cabin conditions. I didn't believe we should spend a lot more time discussing the situation before getting the passengers off the hot aircraft. We reached agreement as a crew; and my understanding was that the Captain communicated all of this to dispatch and Maintenance Control.We ran after landing flows/checks to begin securing the aircraft. All of the passengers deplaned. We stayed with the aircraft for approximately an hour after making this decision; while the passengers were deplaning. The mechanic had not begun any more work or troubleshooting to the best of our knowledge when we left the aircraft.