Air Carrier operating as a lifeguard flight reported that one ATC facility refused to use the lifeflight terminology when addressing the aircraft.

Narrative

Just prior to pushback we received an ACARS message from Dispatch that we had a liver to be used for transplant on board the airplane and that we were in fact a 'lifeguard' flight. We checked in with ground for taxi as lifeguard Flight XX. They requested confirmation that we were in fact a lifeguard flight. We confirmed. We were told by the Controller that he would add that information to our strip. From that point on using the lifeguard call sign; we were answered and queried by ATC with the lifeguard prefix attached. This continued all the way until we checked in with Denver Center. When we checked in with Denver we were answered with Flight XX. We responded with 'lifeguard Flight XX.' Shortly after we were given a fifteen degree left turn for traffic as 'Flight XX;' again we responded with 'lifeguard Flight XX left one five degrees.' We were curious as to why we were being given a vector off course instead of the other traffic? After being on the heading for several minutes; I queried ATC with 'Lifeguard Flight XX;' how long can we plan to be on this heading. The Controller responded with 'Flight XX another couple of minutes.' After another couple of minutes ATC called with 'Flight XX cleared direct DBQ.' We responded with 'lifeguard Flight XX cleared direct DBQ.' Shortly after this ATC called us; again we responded with 'lifeguard Flight XX.' After several seconds passed the Controller said 'Flight XX contact Denver Center on frequency 120.57;' to which I replied 'Was that for lifeguard Flight XX'? Shortly after; the Controller reluctantly called with 'flight lifeguard XX contact Denver Center on frequency 102.57.' I replied with 'lifeguard Flight XX Denver on 120.57 good day.' This was followed by the Controller saying over the frequency. 'The games people play!' I responded with 'We have to comply with a regulation; so do you. Good day.' This call sign issue continued throughout Denver Center's airspace. After we were handed off to MSP the call signs returned to normal protocol. I want to know what the actual requirements are; as applied to ATC; concerning the 'lifeguard' call sign.