Diagnosis
Food debris or melted cheese/fat has seeped into the gap between the basket and the housing, acting like glue when it cools.
How to Fix It
Don't force it. Plug the unit in and set it to 200°F for 2-3 minutes. The goal is to gently warm and soften whatever is causing the stick, not cook it further. Unplug, put on oven mitts, and gently wiggle and pull the basket. It should release.
If That Didn't Work
If something like melted plastic is the culprit, warming won't help. You may need to carefully work a thin, flexible spatula or butter knife around the inner edge of the basket to break the seal. Be very careful not to bend the basket or scratch the interior.
Heads Up
Forcing it can break the release mechanism or the basket handle. Always clean the basket and the inner ledge where it sits after each use to prevent this.