- Take the cable back to the store. Have them plug your cable into one of their Thunderbolt Displays. If the problem doesn't occur then you know that the cable is not defective.
- Once you know for sure that the cable is not defective then see if there is anything in the hole that may be causing a short of some kind.
https://hum3d.com/360-view/?id=109575
The shutting down symptom leads me to believe that it is trying to protect itself from something. Either over heating or dirty power. Ensure all other peripherals are unplugged.