There is not an easy answer.
Originally the time limits (30seconds, 2 minutes, 5minutes) were at least partly based on preventing engine parts from overheating. I think (but please don't quote me on this) that static overheating is not the primary issue anymore, but slowly progressing deterioration through high temperature creep on the one hand and material fatigue on the other hand. I will refer to both as "fatigue" from now on.
The fatigue life of an engine (and the attached gear boxes) changes drastically with the power draw. The following numbers are made up, but they should be roughly the right order of magnitude:
- Engine life at MCP: 100000 Flight hours (FH)
- Engine life at TOP (5min): 10000 FH
- Engine life at OEI low (2min): 10 FH
- Engine life at OEI high (30sec): 0.5 FH
Then one assumes certain conservative flight spectra. E.G. 1 take off and landing every 10 flight minutes (5minutes TOP and 5minutes MCP six times per FH), 1 OEI low every 100FH and 1 OEI high every 1000FH.
Then one combines the fatigue damages per flight hour from each of these phases:
D=5*6/60/100000 + 5*6/60/10000 + 2/100/60/10 + 0.5/1000/60/0.5= 0.000105
The combined lifetime for this example is therefore:
L=1/D = 9524 FH
This number is rounded down and 9000FH lifetime is put in the manual.
There is an additional level of complexity, because the temperature is lower in new engines than in old engines at the same power. Therefore, the heat creep also depends on the age of the engine. Another level of complexity is the fatigue sequencing (I used the simple Miner-Rule in the example above), which is tested on real engines with very demanding power cycles.
I actually brought this up with other engineers, and we could change the rules to a engine lifetime damage accumulation, or usage dependent flight hour consumption in stead of the time limits. However the current system seems to work fine and we are not sure that there might not be an overheating or similar issue that we don't know about, because it is proprietary information of the engine manufacturers. This would allow the pilots to fly for longer than 5 minutes at TOP, however the lifetime and maintenance intervals would have to be shortened, if this happens more frequently than in the design assumption (e.g. more than 30minutes per flight hour, or more than 18 minutes per flight hour, depending on helicopter manufacturer).