Well this schematic of your A/C heat exchange system is the oddest thing I have seen in a while.
Not only does your A/C system share the engine cooling intake (that's bizarre enough) but you indicate that the sink is connected also? Is this a factory original setup or a PO debacle?
If you system is truly set up like this, I suspect that the A/C pump is pulling air from the sink and losing it's prime. I presume that the sink is a seawater faucet with a hand/foot pump. That pump could be leaking air through it's internal valves. Or, even more likely, when the sink pump is activated, it can pull water from the A/C loop and allow air to enter the sea water A/C pump. These pumps will not re-prime themselves.
I have a similar setup where my A/C intake and strainer feed the A/C pump and also a wash-down pump that supplies water to both my anchor locker (for wash-down) and to the galley faucet (rinsing dishes). In order to prevent the wash-down pump from pulling water out of the A/C loop I have a check valve in line with the A/C pump.
My engine cooling is entirely separate, as I believe is the best practice.
To test if the sink pump is sucking the A/C loop dry and causing the loss of prime should be easy. I suspect that this would occur when the A/ C pump is NOT running.
I suppose that the engine loop could be an air source also, but if that is the case, the air leak would have to be before the raw water pump. The raw water pump with it's rubber impeller would not allow air or water to be pulled from the engine heat exchanger which is down-stream from it.