Sounds sort of scary if your engines are all threatening to pack in when you are in DP mode.
Lot of good advice already given.
I had a problem on one ship, I had to change a main Engine cylinder head that was blowing, afterwards I ran up the engine and everything appeared fine. When we came to sail and some load came on the engine the cooling system airlocked and we lost all the pressure and I was furiously venting air everywhere I could find and managed to keep the engine going.
Eventually I worked out what had happened (every time the engine had been drained down for about 15 years since the ship was built).
The jacket water leaving the engine went to a three valve, oneoutlet went straight to the engine driven pump suction, the other, up to the deck head, then down to the jacket cooler and back to the pump suction.
When the engine was drained, all the water drained out of the cooler, when the engine was filled the cooler and pipes to and from it, remained airlocked. Everything worked wonderfully so long as the thermostatic valve was fully bypassing the cooler. As soon as the engine warmed up under load it pumped water into the cooler, displacing the air back into the pump suction, promptly stopping all the water flow.
I would check for air vents/ run downs on the coolers and engines and pumps and make sure they are all open all the time unless the maker's manual says different.
Secondly, check out the pipe diameters, are there any reductions in diameter that could cause very low suction pressures at the Pump??
Usually there are air vents from the pressurised, and high points of the engine, back into the air space in the expansion tank and a run down down line from the bottom of the tank to the pump suction, was a mistake made connecting the pump suction to the air space above the tank, so that the pump draws in air all the time??
What about the flow control orifices, usually CW systems have several flow control orifices in them, are they in the right places and the correct size???
You should have a positive head from the expansion tank at all points in the system, with the pumps running or stopped, if not find out why.
Does the problem happen at full load, light load or all the time?
If it is load specific, look at the pipe work around the thermostatic valve/ cooler/coooler bypass be3cause the problem will be there.
Good luck, I hope some of this helps you and let us know what the problem was and how you fixed it.
It is always better to ask a stupid question than to do a stupid thing.