Crab said, "Nick's information would conclude that it is once only in the life of the engine and after it has been used the engine is irreparably damaged and is destined for a gradual decline in power output." Actually, your guidance to pilots is right on, but perhaps the concept of "Harm" versus "Use" needs clarification.
The idea that the helicopter is an immutible collection of objects, likely to do what it does forever, is not generally correct. Every operation "Harms" it a bit, some operations hardly at all, others with more rapidity. When you run your car, you "Harm" your fuel level, but you can periodically repair and renew it. Each cut with a saw blade dulls the blade, at some point it is not fit for service.
At 1000 hours of life in a 1000 hour part, the harm has reached a level that tells us it is wise to change it, but the part has adequate safety at 999 hours to fly the next hour.
But hours do not harm the part, the stresses on it do. More stress, less life. The stress is driven by the classic things, load factor, speed (rotor stall), gross weight, extreme CG, high altitudes, high power. We at the factory guess the way the aircraft will be flown (we call it the fatigue spectrum) by saying that each hour, the aircraft will fly x% at cruise, y% in climb, z% in hover, and that it will bank at 30 degrees p times, at 45 degrees Q times and so on. This list of educated assumptions is massed, and the test engineers then calculate the accumulated fatigue damage on the parts (fatigue damage is the "harm" Crab mentions).
When you operate, you do what you must, and the banks, speeds, altitudes and weights all sum to pull beans from the jar.
Transcients are established to cover the odd corners, where a slight increased torque or power might be seen, but where the manufacturer has confidence that a few of these in the life of the aircraft won't be enough harm to matter. Generally, we use transient power only as a cover for the oops! and not for actual usable power. We test the transients to show that a bunch of them during the overhaul life are not so additionally harmful as to cause concern. Use them as inadvertant exceedences, not as allowable surges, I think.
rotorspeed, all systems on the helo have some life inferred, transmissions, certainly. The TBO is calculated by figuring out when the beans will disappear, based on the assumed usage spectrum.
Generally, the longer the life, the stronger the part or system, of course. If the aircraft has lots of time change components, at low life, it is somewhat more marginal than one with few, long lifed components.
The ultimate limitation is usually the static strength of the part, which is the place where one pull at that level produces a break or permanent bending. Generally, a part can be stressed at 50% of its static strength for a great deal of cycles without any permanent harm (we call this the "Endurance Limit" strength.) For Sikorsky helicopters, we try to be sure that all components are below this endurance level for all level flight conditions, but maneuvers might pop up into the fatigue area.