Diagnosis
The internal cord wires are fatiguing from repeated tight twisting. The insulation is binding.
How to Fix It
Unplug. Fully straighten the cord. Gently rotate the entire iron in the direction that untwists the cord. Do this regularly as maintenance.
If That Didn't Work
The strain relief grommet inside the handle has cracked, pinching the wires. This requires disassembly and grommet replacement to prevent a short.
Heads Up
Never yank the cord from the wall by pulling the iron. Always grip the plug. A broken cord here can expose live wires.