Hi: It sounds like a plumbing leak. To test for this, get a 0-200 psi pressure gauge and put it on a hose bibb outside the house, but that’s hooked up to house plumbing. Now turn off water to the house. Make sure nobody is running water. If pressure on the gauge falls off right away when water is turned off, you know there is a leak someplace. Now, if there is a leak, do the same thing with the heater. Put a gauge on the drain valve and shut off the water to the heater. Does pressure fall off?
If you had a water meter it would be, simply watching that meter for a few minutes to see if it moves when nobody is using water. A simple test that could work for you is just to feel both hot and cold lines on top of the tank when no water has been run for a while. Both should feel warm. If the cold side is cold and the hot is hot, water must be flowing. Even if you only find the cold side being cold, it could mean the relief valve is leaking. As long as there are no buried hot pipes, finding the leak shouldn’t be too difficult. 😉
ps. If you get scalding hot water, the problem could be something else entirely.