Diagnosis
Grease and food debris have built up in the basket guide rails or around the basket release mechanism, acting like glue.
How to Fix It
Let the unit cool completely. Hold the outer 'cooking pot' firmly with one hand. With the other, press the basket release button firmly and jiggle the basket handle side-to-side while pulling straight out. Do not yank. If it moves slightly, work it out slowly.
If That Didn't Work
You may need to loosen the debris. Unplug. Carefully pour a small amount of hot, soapy water into the gap between the basket and the pot. Let it sit for 10 minutes to soften grease. Then try the jiggle-and-pull method again.
Heads Up
Never use tools to pry it out. You can warp the basket or damage the non-stick coating. Clean the basket rails and the inside of the pot thoroughly after every few uses to prevent this.