I'm surprised that no one has mentioned this:
The pressure relief valve can also leak when the airspace in the tank is gone. There should be air above the valve to allow for expansion when the water is heated. If no airspace then the expanded water is forced out the pressure relief valve.
To ensure a proper air chamber: Shut of water to system (either at the tap if on city water or turn off the pump. Open the pressure relief valve and a hot water tap at a sink. If no water runs out, the air chamber is OK and there is another problem, likely the valve. IF water runs out wait until the water stops running,close valve, turn off hot water tap then turn on the water pump or the city water. This procedure will restore the air in the tank.