If the plasma arc extinguishes while trying to cut, it could be that the arc has not transferred and the plasma cutter still thinks it is in pilot mode. While in pilot mode the plasma cutter will limit how long the machine is on for safety reasons.
In order to ensure that the arc transfers to the workpiece and into cut mode, make sure that there is a good connection from the work clamp to the workpiece. Grind off any rust or paint in a small area, and hook up the work clamp to that spot. The plasma arc can cut through paint and rust, but the work clamp needs to have contact with bare metal.
Also remember that electricity is lazy and takes the path of least resistance. Make sure that the torch is close to the workpiece. All Miller plasma cutters come standard with a drag shield on the torch, so go ahead and drag the shield on the piece you are cutting. The drag shield provides the optimized standoff height for cutting.
Engineering Technician, Plasma Products