Let me preface by saying I'm not qualled in the R44, I have a short amount of time in the R22. So why am I posting here? I currently own and fly a fixed wing plane with an engine which is time limited for max power.
The E-225 engine in my plane is able to produce 225HP at 2650 for 2 minutes. Max continuous operation is WOT at 2300.
For any installation, this can be limited even more by the airframe mfg, but it cannot be exceeded due to the engine type cert. What is certain is that heat kills. The hottest part of any IC Otto cycle engine is the exhaust valve stem, seat, and valve guide. The next area of concern is the top of the piston, which is a hypereutectic alloy of Al, Si, and other goodies.
Extracting heat from a Helicopter engine is always a challenge. No matter how well designed, the cooling flow, and air path will always create hot spots. The TBO is a function of the best case of the hottest part of the engine. For the big bore Conti, the main bearings, and the cam bearings are usually good for > 4000 hours. However, the cylinders, valves, pistons and rings are much more highly stressed, which is supported by the number of cylinders replaced, and the 'top overhauls' made on many engines.
I will opine that there is a combination of systems that limit the maximum HP to 5 min or less. However I know that most of the restriction is going to be related to heat generation in the engine.