I found out this tip while on vacation. Sometimes micro-scratches from daily wear and tear will dull a stuffed animal's eyes, but I got sunscreen on one of my plush's eyes and the compounds in the lotion dulled the surface. I used a nail buffer by Revlon, the Crazy Shine Nail Buffer, you can get at Target or most drug stores.
Buff the eyes carefully with the grey foam back of the buffer in a circular motion, this will "roughen" the surface and it will look satiny or even velvety. Then, buff with the white side using the same motions. This will restore the shine to your plushie's eyes!
I would recommend testing this in an inconspicuous area of the eye, maybe near the fur, before buffing the whole eye, just in case this method doesn't work with the particular type of plastic you have. I'm so glad I found out this tip that turned my toy's dull, dead eyes back into shiny, lively ones!