Wow, what a cool car. I love Country Squires'.
I have a few suggestions to your problem. In last months Hemmings Classic Car, in the tech talk section, there was a question just like yours. The answer was similar to dead horse', except the expert told of how modern radial tires put more stress on the outside of the steel wheels made in the period before radial tires. Radials are constructed such that the cord runs from bead to bead. This construction makes the side wall very stiff as apposed to bias ply which ran the cord around the center (tread) of the tire and the side wall was allowed to flex. This softer flex placed more energy towards the center of the tire where it would roll but keep the tread in contact with the road. Radials perform better because the construction keeps more force on the center of the tire and there is less chance of the tire rolling. Now I know wheels are strong, but remember that they are welded and can deflect more with age. Check the trueness of each wheel which looses the caps.
Another trick stated by the Hemmings author was to try to secure some Velcro to the wheel and the wheel cover. He said this was a cure some one had written in to the magazine. Might work. But I have another idea which worked for me many years ago: I had a 1976 Monte Carlo which I bought nearly new. It had Turbine Wheels which were poly cast (a process where a vinyl overlay was cast directly on to a steel wheel. It was very popular in the 70 and 80's). The center caps started falling off on the outside wheels during cornering. I must have bought 5 or 6 replacement center caps until I tried (gluing) on the covers with marine silicone (RTV) sealant. I chose clear, and put a thin bead on the outside of the center cap, and placed the cap back on the wheel, and let it set over night. After a month, I had not lost a cap. Thinking that I might done too good a job, I tried to pry off one of the caps. It was on good, but with a little force the seal broke free and the cap came off easily. I cleaned the residue off and re sealed the cap, and never lost another in the next two years of owning that car. Hope this helps.
I think the old wagons are becoming very valuable. Imagine how many were driven to the death, and you have one that survived. Very cool. | 
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