Radio keeps shutting off every 50 seconds

[0427amr]

I have a 2000 ford explorer 2wd, when I got it, it had a number of electrical issues, but I'm stumped on this one.
I replaced the connector that goes into the stock radio because it was damaged and no longer fit, I noticed that the people before me had already swapped them out. When I connected it the radio worked perfectly, but then it shut off and immediately came back on. It does this almost exactly every 50 seconds (I timed it). It does this with the original radio and the newer radio I have. The wire connections look good. I don't know if I should go in and solder the wires, look for a bad ground or what. I just don't know where to go from here.
Any help would be appreciated.

 

[Mbrooks420]

I would cut the switched power and ground wire and reconnect them making sure you have a good connection.

These would be my first suspicion. You could also temporarily connect the switched and constant power wires to the constant power feed.

 

[donalds]

Mr Brooks pretty much nailed it