Thanks for your rapid responses.
The problem is 20 years old block paving still in excellent condition (and yes vibrated down when installed) and also vibrated during the sanding. No sinking anywhere because the area was surrounded by paving stones sunk edge-on into the ground when first dug out so the rubble/crusher-run/sand could not migrate.
Last year I paid a specialist firm to clean, weed-kill and resand then seal with a polyurethane liquid. They advertised that a stage in sanding was to use a plate vibrator to shake the sand down "into every nook and cranny" before sealing. However, the operators did not do the vibrator bit. Within a month much of the sand had disappeared form the area where I drove the car onto the hard standing. Looks almost like wheel tracks.
I believe that they only brushed the sand into the joints and it sat at the top of the joints, giving the impression that they were filled up and held there by the sealant.. This allowed slight movement which did permit the shallow layer of sand to drop deeper between the blocks.
I propose first vibrating the whole area (about 33 sq. m) to make all the sand drop down between the blocks then keep sanding and vibrating till no more sand goes in. Sweep clear the re-apply sealant.
This is plan A. But I am only a basic DIYer and would be glad of more experienced advice. Hence the request about the actual machine to use. HIre sites show petrol and electric, with three weights of machine to choose from.