Why does colour rub off a pressed powder?

It is adhesion and compatibility, not a pigment that is inherently loose.

Three causes. The pigment does not bond to the platelet fillers — talc, mica — so it sits at the surface and wipes away. The formula is low in oil, so the powder has nothing to grip with. Or the loading is above what the base can carry and the surplus becomes loose dust.

The fixes follow the cause. A treated pigment improves compatibility with the oil phase and lifts adhesion. Adjusting the base — more platelet filler, or a filler with better adhesion — gives the pigment something to hold on to. And keeping the loading inside the base's capacity helps, using a high-strength lake so you need less.

If the problem is a liquid foundation wearing off rather than rubbing off, look at the film former and the adhesion promoter instead; the pigment is usually innocent. Quantify it with a rub test at fixed pressure and stroke count, plus a wear test, so comparisons are numbers rather than impressions.