Welcome to the Axiom forums Dave M.
The EP350 should not cut out. It sounds like the input on the back of the sub is damaged and needs to be replaced. It also looks like the connector on your subwoofer cable creates a very tight connection with the female input on the sub. This is very common. The Canare/Taversoe connectors that are used by Blue Jeans Cables create a great connection without fitting too loose or extremely tight.
As to the buzzing it can be caused by two things - either a ground loop or a defective subwoofer. Sounds more like a ground loop to this point.
As your first step into troubleshooting the "buzz/hum" can you disconnect your subwoofer completely from your setup.
With only the subwoofer plugged into the electrical outlet, when you turn it on does it hum? If it does then the subwoofer amp is faulty, if it doesn't there is a ground loop in your system. The latter we can fix with some easy troubleshooting steps.