Enroute Controller described a loss of separation event when a military fighter initiated an unexpected descent due to aircraft problems without informing ATC of details. The reporter indicated that the aircraft should have declared an emergency.

Narrative

An F15 [was] climbing from FL410 to FL450. Told me he could not hold altitude. I re-cleared him to FL390. He descended through FL390 and kept descending without telling me. I asked him his altitude. He told me he couldn't maintain altitude. I asked him what he needed to descend to. He said FL250. He also lost all speed of the aircraft. Another aircraft was initially 10 miles behind him at 450 KTS climbing up to FL430. The second aircraft was overtaking the first rapidly. I turned the aircraft 90 degrees to the right to try and keep 5 mile separation. They passed with about 4 miles of separation. All this happened with heavy traffic volume and high complexity due to weather. If I hadn't been so busy I could have quizzed the F15 more about the problem. This would have led to a quicker realization of the potential problem of loss of separation due to loss of altitude and loss of speed. Or if the F15 had told me how bad the problem was; or declared an emergency; I would have turned the aircraft sooner. Military aircraft should declare an emergency when they cannot hold altitude and/or maintain speed.