If your paint is really dry, I'd expect the fingerprints to be body oil left on the model when you touch it. Other than advising you to touch the model as little as possible, maybe varnish or coat(s) of Future could help. I expect you find this problem more with flat finish than gloss ones... And it's always more difficult to remove the prints from flat surfaces than glossy ones... The flat paint is, at a microspopic level, very uneven, a bit like a mountain range, and oils left in the 'valleys' will be hard to remove. Varnishes and Future will even out peaks and valleys and make it easier to get rid of the prints.