There's a very good reason why credit cards are made of plastic -they are extremely durable and you can find them in your wallet easily. Good quality clear plastic business cards are the same. With plastics technology improving all the time, plastic credit cards can stay flat, even after being in the back pocket of your jeans all day and they will even survive going through the washing machine followed by the hot cycle of a dryer!
Of course clear plastic business cards are a lot more expensive than a cheaper paper card. Just like paper they come in different weights, but they are all much more durable than paper. They still won't cost you as much as going through the old-fashioned local printer process.