[GoldenRivet]

From learn to fly airplanes web site. (Im without the benifit of consulting my own multi engine lesson plan at the moment for a brief explaination)

"There is a dramatic performance loss associated with the loss of an engine, particularly just after takeoff. Any airplane’s climb performance is a function of thrust horsepower which is in excess of that required for level flight. In a hypothetical twin with each engine producing 200 thrust horsepower, assume that the total level-flight thrust horsepower required is 175. In this situation, the airplane would ordinarily have a reserve of 225 thrust horsepower available for climb. Loss of one engine would leave only 25 (200 minus 175) thrust horsepower available for climb, a drastic reduction. Sea level rate-of-climb performance losses of at least 80 to 90 percent, even under ideal circumstances, are typical for multiengine airplanes in OEI flight."

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the above paragraph refers specifically to climb performance.

a properly loaded multi engine aircraft being operated within standard atmosphperic conditions with One engine inoperative would be capable of maintaining straight and level flight, however, given the loss of power it would be incapable of climbing beyond its maximum single engine altitude.

when you add the adverse loading condition to the equation

and you add the hot or humid conditions contributing to high density altitude

the result may be that the aircraft is only capable of a controlled descent. (this is very frequently the case when weight loading issues are involved.)