For Part 29 helicopters, the power assurance check is used to measure the engine against a standard, and to therefore assure the airworthiness of the helicopter. The performance is not necessarily assured if the engines are not up to spec, but also the cause of the low power might be a condition that affects the engine's airworthiness, in that it could be precourser to an impending failure.
Generally, consistent below spec power is reason to ground the helicopter.
Some comments:
1) Marginal engines, quite fit but right at spec, will by the forces of nature measure below power half the time and above the other half. This is the normal statistical fallout of any measurement, and not a sign of sickness. Some machines are certified with a daily averaging method to allow reasonable assurance even if a particular check is low, as long as the rolling average is acceptable, and there is no obvious other problem. I think a zero margin engine can be operated in the face of it failing half its checks, as long as documentation like a recorded history supports the reasonable assumption that it is simply borderline.
2) The OAT/FAT gage is a prime contributer to this scatter, since turbine engine power varies by about 1% power for each degree C. That means that one degree of variability on the gage could spell doom for an otherwise healthy engine. The typical bi-metalic temp gage is not really designed to provide the accuracy we ask of it.
3) the pilot procedures during the check are critical, and any sloppy handling or hasty reading could make acceptable aircraft seem unhealthy. The biggest problem is facing squarely into the wind, so no reingestion of hot exhaust occurs. One degree of OAT rise is about 4 degrees of engine temp, so a little reingestion is a bad thing. Checks done on the ground have more scatter, and the possibility of more hot ramp air finding the inlet than fnding the OAT gage, so many helos have in flight power assurance procedures, where clean air and steadier conditions help reduce the scatter.
4) Below margin engines might otherwise be quite safe, just a bit more eroded or dirty. Sometimes, engine manufacturers file letters and maintenance procedures to allow below spec operation, as long as no other condition is at fault. This allows the pilot the assurance of continued engine safety, but not adequate aircraft performance. For below spec operations to be legal, there must be flight manual performance procedures that allow the pilot to determine the flight performance with the amount of degredation folded in. This is sometimes done by providing a rule on the chart, such as "For engines below spec by x percent, enter the chart 900 feet higher than ambiet for each percent below spec" Thus the normal chart allows the pilot to precisely calculate. In US Military operations, this is quite normal, and up to 10% power loss is not a grounding condition (15% in the case of the CH-53E!)
4) The situation can be reversed, so that the pilot could be provided with above spec charts to take advantage of more than spec power.
5) If the failing power assurance is a relatively sudden drop, say more than 2 or 3 % in a day, it is almost surely a sign of a maintenance problem. Salt encrustation, bleed valve leaks, dirty engines are often the cause. Sometimes, an internal engine crack could be allowing hot gasses to be strangely circulated, and the drop in power could be early warning of a catastrophic condition just about to happen.