Waiting for an answer myself :)

Mine are much larger than fist sized but they do sink over time. Usually I expand my beds outward by a few inches a year anyway so I can buy more plants but at some point i am going to have to call a halt to that.

Initially we used very well buried black plastic landscaping borders underneath my rocks to stop turf grass invasion- I came from a climate where that was a problem and I knew no better. Turns out that isn't all that much of an issue for me here so every time I expand a bed I remove a section of it, but it did help stop the sinking. Right now I am experimenting with laying a row of old bricks under some of my rocks so that weedeating is a tad easier, but then we found a huge stack of old bricks in the woods when we moved here. I expect they will sink over time as well. Eh, it keeps me busy.

I look forward to any solutions offered- I have over 400 feet of rock borders and I'm not getting any younger. As you can see here on "bed expansion/rock moving day" it's a huge heavy job.

As everyone probably knows, I am not a fan of rocks, bricks, or other bordering materials that are raised above the surrounding grade, but I'm certain there will never come an end to it. In most cases, if the material is flush with the grade and wider, it will look better. In landscaping, much is about proportions. Considering the typical brick edging has a thickness of barely more than 2", it looks almost as thin as a knife edge raised above the surroundings. Since it is usually "retaining" nothing but air, it looks a bit purposeless. If the raising was retaining soil or mulch, it would make more sense, but still look wrong (weak and fragile) as if trying to retain grade with manufactured eggshell. A border that uses the brick length -- 8" -- is a dimension that looks much more capable of retaining earth. If its retaining a grade change it should be positioned as one would do a curb (a mini-retaining wall) .... not sticking up in the air. If there is no grade change, it will look best set flush -- an inlaid border (mowing strip.) In the case of using rounded rocks, it looks better if their tops are uniformly set relative to one another and that the whole strip is not raised, but set as one would install cobblestone. Too, a single row of such stones is going to appear very weak. It would look better if they are installed to be a cobblestone border that is 12" wide or greater. Like all the other hardscape, one wants to correctly install it in the first place as it would be a lot of work to redo.

Generally, the process of installing stones is to excavate a trench a few inches deep in which will be placed a crushed aggregate base of about 3". (Where I live it would be called "paver base," which is usually made of crushed concrete. It is basically a coarse, nutty sand with chips and dust in it and it packs down tight and hard. "Driveway gravel" could also be used.) On top of this would be placed a varying 1" layer of any sand which allows for adjusting the rocks such that their discrepancies in thickness can be negated. At the end, more sand would be added over the top to fill in the gaps between stones, as if like powdered mortar, keeping them in place. For added stability, a strip of woven, polypropylene landscape fabric as wide of the trench itself can be used at the bottom of the trench to give added long term stability to the overall structure. It would help prevent the border from sinking or moving. Landscape "fabrics" that stretch or can easily be torn cannot be used.