DIAGNOSIS: The plastic drive coupler on the jar has partially melted or deformed, mechanically locking it onto the motor shaft.
FIX: Do not use excessive force—you'll break the glass. Unplug the unit. Apply a few drops of food-safe lubricant (like mineral oil) around the seam where the jar meets the base. Let it seep in for 10 minutes. Hold the base firmly with one hand and use a rubber jar opener or silicone oven mitt for maximum grip on the jar. Twist counter-clockwise with a firm, steady jerk, not a slow pull.
IF THAT DIDN'T WORK: If it's truly fused, you may need to sacrifice the jar. Carefully use a heat gun or hair dryer on low to warm only the plastic coupling at the jar's base for 30-45 seconds (avoid direct heat on glass). Try twisting again. As a last resort, you might have to break the jar to save the motor base—call KitchenAid for a jar replacement.
HEADS UP: This happens from running the blender too long, overheating the contents, and not removing the jar promptly after use. Always remove the jar right after blending, especially with hot mixtures.