This sag is also known as "rear end separation." If you do a google search for "airforums rear end separation" from outside the forums, you should find several hits.
It is typically caused by water that runs down the outside of the rear of the trailer, hits the bumper trunk, and is directed quite literally into the endgrain of the rear-most sheet of plywood. The wood eventually rots away leaving a gap. The rear of the shell is still bolted and riveted to the rear of the frame, but without the wood there, they are free to move relative to one another. Eventually the bolts fail, any rear hold-down plate rusts away, the rear-most cross member disintegrates, and the rivets in the shell tear out. At this point, the bumber and the rear of the shell can move completely independent of one another. Since the shell is not holding the frame up, it will flop around, and may eventually fail completely due to fatigue. This is when you get the serious droop/sag.
If it has gotten this far, it is usually obvious. If it is in the early stages, then you can step up on the bumper and just bounce a little bit. The shell and frame should move together. If the frame deflects under your weight, but the shell remains stationary, then you have the beginnings of the problem. You can also look into the cabinetry in the rear of the trailer that covers up the rotting plywood and take a look at its condition. If the plywood is solid, then you probably don't have a separation issue.
The older the trailer is, and the wetter the environment it has lived in, the higher the likelyhood of floor rot. Design wise, it hasn't changed much since 1969.