When you push the handle forward does it snap into the detent??, the spring could be broke, or the notch worn and not keeping it in the locked position.
The springs, and latches, and inside assemblys are common on e bay, and not that much $$ for NOS --except for open cars.
Lock it and watch the inside handle, if it moves to unlocked when you move the outside handle take the door panel off and look at the spring/ detent where it inside handle attaches (the inside part is the same for many years, my 36 has the same one my 46 had)