Fresh water pressure, help
Sounds like you are on the right track...must be a leak.
The mystery is why not the hot water side as well? The pump should provide pressure for both sides of the system initally. Maybe a check valve in the hot water side?
You can track down the leak by looking for water dripping/running into the bilge or, open up the system at some point and insert a temporary plug. Turn on the pump and see if it holds pressure. If so, then the leak is likely further down the line. If not, it must be between the temp plug and the pump. Repeat the process until you isolate the problem.