Diagnosis
Food residue or sugar has solidified in the locking mechanism. The jar's drive spline is jammed into the base's coupling.
How to Fix It
Unplug the base. Hold the base firmly with one hand. With the other, grip the jar handle and the lid. Twist the jar counter-clockwise (left) while applying steady upward pressure. Do not rock it side-to-side. If stuck, pour hot (not boiling) water around the jar's drive spline to melt residue, then try again.
If That Didn't Work
The plastic locking collar on the base may be deformed. Inspect it for cracks. You may need to disassemble the base collar to release it. This is a repair job.
Heads Up
Never force it by hitting the jar or using tools. You can crack the jar's drive spline or damage the motor shaft. The twist-and-lift motion is key.