We have an '04 Prius and an '06 Prius. The plastic panels (6" x 4') under both cars got so full of lime (from gravel roads) that they were sagging. I removed them and cleaned them but they are deformed so I do not plan to reinstall them. The only rusty area under the cars is where they were kept moist by the lime. Do these panels serve any purpose other than possibly improving aerodynamics? (and, of course, collecting dirt) If they actually protect something I will consider replacing them. Otherwise they will stay off.
It definitely improves aerodynamics. If you ever get a chance to look at a race car, look underneath... it's buttoned up tighter than a nun's blouse. You can do this two ways... leave the panels off and see what gets damaged, or replace the panels and have the piece of mind. While most electrics are well sealed, I'm not going to gamble on that. Electrical problems are the toughest ones to diagnose...