Someone else suggested a good idea - make companies link to their previous request. Or even better - don't allow companies to post the exact same listing for months in a row. The actual behavior you're trying to root out is a company listing a position that isn't real - so just don't allow them to list the same not-real position over and over.
I don't know if that can be enforced, though it should be easy to script up something that checks this. But you're not going to enforce anything anyway, and I think this gets closer to actually what we want to achieve.