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Normally I don't chime into radio issues cause I know we have better people for this. But clear something up when you unhooked the speakers how did you do that? I would of took the wire nuts off every wire and disconnected each on on the stereo side of the pigtail. Then either capped them off or put tape on them and only have a new hot wire wired into the power and memory and then a new ground. If the radio still shuts down and powers back up would say it's a radio issue itself and might be time for a replacement. Unless it's a bad connection right in the back of the radio.
ok, so we are worried about power not speakers. a bad ground is still a possibility, i know they've caused me a ton of head aches before. Another quick test, run a ground directly from the battery as well. you may want jump the red and yellow together (main power from battery with both yellow and red wire twisted to it) in-case its losing power. if that doesn't help i would get a multi meter and check battery while someone put it in revers, you could have something lose and shorting out causing the issue. If straight wiring it to the battery fixes it then check each wire for power while someone put it in reverse and look for a voltage drop. also check original negative for voltage drop when putting it in reverse. if you find one of the wires is losing voltage start tracing back to the fuse box
Connect your voltmeter: positive to bare cab sheetmetal and negative to the battery negative post. Switch on the radio and accessories as usual then step on the brake and watch the meter. What happens?
Get rid of those quick connectors. Solder and heat shrink all of your connections. Run an auxiliary ground from the dash to the kick panel bus. Run another auxiliary body ground to the engine block. Run another one to the radiator support and back to the battery.
Poor cab ground. The cab is actually grounding through the brake pedal arm and connecting pieces. Move the brake pedal with your foot and the ground path is interrupted. Follow Vile's advice. At minimum you need the following grounds to function perfectly: 1) battery negative-to-engine, 2) battery negative-to-right (passenger side) frame rail, 3) back of engine right side cylinder head-to-cab sheetmetal, 4) battery negative-to-radiator support.
basically your cab isn't grounded at the moment. What they are telling you to do will guarantee your cab is grounded well, he is talking about the current grounds you mentioned. You dont necessarily have to make new holes. On my truck i ran a ground from the battery to the engine, ground from the radiator support (where headlights are grounded) to the battery, A ground from battery to frame, a ground strap from engine to the firewall of the cab, and i also have a round strap from the back of the cab to frame (stock location) Also make sure all your grounds are clean bare metal
i would take that ground off the valve cover as its not really a good ground. attach to the intake or block. theres no bolt holes in the passengers side read head?