So, what is the question? Of course, it stays on. It is a problem only ham radio operators suffer from, and the problem is in your DC power supply and using a radio designed for a car in your house.
The problem lies in your DC power Supply, your Astron. It is outdate still using 1960's grounding topology. Your DC Negative output terminal is bonded to the chassis of the DC power supply. That does two nasty thing hams love because it gives them problems to fix.
First, you lose AC and DC electrical isolation required by all electrical codes placing your radio in a nasty daisy-chained ground loop. Now any noise flowing in the AC ground system is now flowing through your DC ground system (your radio). The two mix together, have an orgy, and produce noise. One big party with both the front and back doors wide open for anything to come inside and look around. You're in a Ground Loop!
The second thing it does is it turns your whole ground system into a DC negative circuit conductor. You no longer have a ground. Your car radio power and ground topology are two-wire vs modern 3-wire systems. Inside your radio, the DC negative is bonded to the chassis of the radio. A huge no-no in the modern world. Compounding the problem is your DC power supply with the chassis bonded to DC Negative again. This places Ground in parallel with your DC negative return conductor. By doing that, you no longer have Ground, you have a DC circuit conductor you call Ground.
So, when you lift the DC wire from you power supply, your coax shield and station ground are there to take up the slack Stupid simple to fix, so simple most hams have not figured it out in 50 years when the electrical world changed and went to 3-wire topology. Open that antiquated Astron and remove the jumper that bonds DC negative output terminal to the Chassis. Do that and all the problems go away. Problem is, it can eliminate a lot of noise problems you guys like to waste a lot of money and time fixing with band aids rather than addressing the real problem. Gives you something to do, I guess.