Perhaps this demotion of your contract need not be taken personally? Perhaps it's a move for the business to stay afloat?
Do you get the feeling your bosses expect the business to fail in the next six months?
Did your coworkers have their contracts demoted too? Is everyone's paycheck up to date?
If you stick around it's likely for the bosses to ask you to train the following guy. Let them take their time hiring one, in hopes he'll be qualified for the job and will not cause you to tear your hair out.
However if I were to read between the lines of the way they demoted your contract, it indicates they would not mind if you leave now. They may even hope you'll give them a reason to fire you. So if you already have another place you can go to work, you might as well go (unless you believe early departure would result in a bad reference).
It helps if you avoid doing anything that will get you a bad reference.