I have a fine pair of compasses that I inherited from my grandfather, who was an engineer. They must be well over 100 years old, but I have the same trouble with them that your son has with his. This is obviously a long-standing problem that makers of compasses have failed to crack. The only advice I can give is to stick the point of the compasses very firmly into the paper, and then trace the circle slowly, in stages, without applying much pressure. It may be necessary to go over the circle more than once to make it clearly visible.
Sorry I can't be of any more assistance with the problem!