Bayer brought up a good point about reactions between the paint and the plastic (and one I should have mentioned, seeing as I work in the plastics field!) Sometimes the solvent in the paint may react with the plasticizer in the plastic (the oil which gives the plastic it's flexibility) and cause a small amount of the plasticizer to leach out. As this plasticizer is usually a phthalate based oil, it will never evaporate, meaning the paint will never dry. But this should really only happen with enamels which use a spirit based solvent. Acrylics generally use water as a solvent, which should not affect the plastic at all.

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"The future's uncertain and the end is always near." - The Doors "Roadhouse Blues".