Let's assume that the cages and balls are installed properly. Let's assume that everything is adjusted properly. Let's assume that the non-drive side lock nut is locking the non-drive side cup properly. That would leave only one thing, in my mind...
Are the bottom bracket threads or the cup threads in good shape? If not, under use, it is possible that the entire cup is slipping on or jumping over the threads. A cracked bottom bracket shell would also contribute to the problem. Other than that, what else is there to consider?
Again, this thought assumes that installation and adjustment is done properly.
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"98% of the bikes I buy are projects".