Step 1: Make sure you have selected the correct design for your particular CNC cutting process.   If you are using laser or waterjet you want the closed cut path version of the design work.  If you are using a plasma or router you want the open closed cut path version of the design work. 

Step 2: Make sure you are using the right tip and amperage.  If you are utilizing a plasma cnc you will want to make sure you are utilizing a fine tip consumable of between 20-40 amps to ensure that your cut path is less than .0625″ wide.   (the smaller your cut width the better your cut results will be). 

Step 3: Often times, the cause of artwork falling out unexpectedly is excessive heat or buildup.  You can mitigate this probelm by spreading out the order of your cut paths so each path is not being cut one after another in a small section.  This will reduce heat build up and minimize the possiblity of sections falling out.