Sharpie permanent marker is designed to be long-lasting, but it's likely to be truly permanent on some materials more than it is on others. Hard, non-porous plastic isn't always the best surface for Sharpie use, as the ink often rubs off in a surprisingly short time. Keep your Sharpie lines lasting longer by prepping the plastic an treating the marker ink for maximum staying power.
Wash the plastic with dish soap to remove all traces of dirt and oils from fingers (or elsewhere); removing this things will make it easier for the permanent ink to adhere to the plastic's surface. Thoroughly towel dry the item.
Rub the area where you want to write with the Sharpie with sand paper, provided the plastic is opaque and don't have a shiny finish you could ruin. This will make the surface porous enough to help the ink soak in to the surface and stay in place.
Mark the area slowly. Move the pen or marker fluidly, but go slowly to allow more time for the ink of the pen to soak into the surface. You can also create this effect by retracing your designs or words three or four times.
Let the ink dry for a minute before you handle; though it might not seem it, the ink needs a little time to dry before it is fully cured and won't smear of with the handling of a moist hand. If the plastic surface is highly water resistant (especially if you couldn't sand it), wait two minutes to be on the safe side; the ink will soak into these kinds of surfaces less than with softer or rougher plastics.
Coat the ink with sealant or laqcuer. If you're OK with covering the entire surface, use a spray laqcuer or varnish. To just apply the top coat to ink itself, apply with a detail brush and use a lacquer designed to be applied by hand. For non-toxic lacquer, use an acrylic lacquer (these ones look like milk when they start and are water-soluable before they dry. Alternately, just use a little nail polish.