With the pressure reduction valve, you also need an expansion tank. If you have one, and it is 20-years old, it is probably shot. Sounds like the classic water expansion problems when the WH heats the water after a shower or any other use, it expands and temporarily raises the pressure. Your old valve is leaking a little until the amount that expanded is leaked out, returning the pressure to something the valve can handle.
An expansion tank has a rubber bag or bladder in it with one side pressurized and water in the other. When the water expands from heating, it compresses the air. When the bladder is shot, it fills up with water and there is no place for the heated water to go but to increase the pressure. Since water doesn't compress, it expands rubber hoses, leaks out, etc.