I'm embarassed and can't believe that it took me nearly 40 years to resolve a recurring problem I've had occasionally with my sewing machine. However, I thought I should share this just in the off chance that there is someone else out there, like me, that sometimes fail to think of the obvious. Please don't feel obliged to self-identify.
Recently, I began trying my hand at machine quilting--I've not quite gotten the hang of free motion, so I'm just trying straight stitches for now. Anyway, I thought I would try using my walking foot for the first time. After every few minutes of stitching, the walking foot would become loose. I'd tighten it and began again, then it would become loose again. I was getting so frustrated until I noticed that the screw that I use to tighten the foot has a little slit on the head. That's when I had my "ah ha" moment.
In my serger toolbox, there was a little screwdriver of just the right size. I used the screwdriver to tighten the screw holding my walking foot in place. By using the screwdriver, I could get the screw extra tight such that it no longer loosened with the sewing vibrations.
Over the years, I've had a similar problem with other sewing feet, but I suppose I never got quite as frustrated with it before now.