DIAGNOSIS Food debris or grease has likely hardened in the basket release mechanism's track, jamming the latch.
FIX Don't force it. 1) Unplug the unit and let it cool completely. 2) Lay a hot, damp cloth over the area where the basket handle meets the main body for 5 minutes to soften the gunk. 3) While holding the release button down, gently wiggle the basket side-to-side as you pull. It should come free.
IF THAT DIDN'T WORK You may need to access the latch. Remove the four screws on the underside of the handle cover (use a small Phillips head), lift the cover, and clean the latch mechanism directly with a soft brush and a little warm, soapy water.
HEADS UP Always clean the basket release area and the corresponding slot in the main unit after each use to prevent this.