Someone dug up a tree or shrub and filled the hole with compost or mulch. While it seemed like a good idea at the time, when compost or mulch decomposes, it has no volume left. In order to fill that hole you will need a mineral based soil. Sand and clay are minerals. Your dirt is probably minerals. Eventually you will have it filled. I'd continue doing what you're doing until it stops. Or you could dig out the 18 inches and refill all at once. If you do that be sure to mound the top of it because even minerals will continue to settle for three years.

Thanks for the input, dchall. Problem is I'm the only one living here for the past 40 years, and the landscape has not been altered in any way. I know that the best solution to the problem would be to just dig up the area and see what's going on underneath, but that would require me to dig a bigger hole than I already have, and that's not an attractive idea. What I may do is to just scoop it out with a trowel as far as it will take me and see what comes up.

Maybe use a post hole digger.

Is it possible there is a spring under there? How about a leaking pipe?