Man, I have spent a month working on this same issue with my 96 Civic Ex. After lots of searching and troubleshooting I found that this post had the most info so decided finally to register and post in hopes of some help.
Originally had a pioneer deck in my car that when I started the car it would not come on unless I turned the car off and back on. Thinking this was a deck issue I got a pretty much brand new kenwood from a friend that sold their 94 civic si.
After installing the kenwood deck after about a week it too started to not come on when I started the car. I would need to turn the car off then back on to get it to work. Then about a week later the radio started randomly shutting off then coming right back on while driving.
First troubleshooting I did was cleaned the battery terminals and took the radio out and re-did the wiring. The problem started up again after a week. So started searching the web did one repair at a time and after a few days to a week problem always came back with a vengeance.
Got under the dash and found that the wire coming out of the acc socket was bound up and the wire was chopped up right next to the black T connector that plugged into the socket. So I repaired it hoping that it would fix the problem but after a few days radio started power cycling again.
Now my civic is a 96 Ex with all stock engine parts car has about 235k on it. I worked as a service advisor at honda for 3 years and at a stereo retail store called cartoys for 3 years as well. All the repairs that have been done on my car have been done by certified Honda techs and all my stereo gear has been installed by certified installers. With that said I have exhausted all possible help from friends to resolve this.
1. replaced the three grounds ( core support to engine, transmission to body, battery to body)
2. Found a 98 civic lx fuse box and replaced ELD
3. put brand new battery in car
4. cleaned battery terminals.
5. repaired the acc socket wire.
6. ran a fresh ground to the radio, also ran wires from the under dash fuse box for 12v constant and acc 12v, radio still did the same thing it did hooked up to the factory harness.
7. hooked both power wires from radio up to the 12v constant off of the factory harness radio still power cycled at random.
8. ran a 8 gauge wire for an amp kit from the battery out the hood and through the passenger door hooked both radio power wires to 8 gauge wire and radio still power cycles at random.
9. bench tested radio by hooking it up to a battery tender for 15 hours and radio never power cycled( I know this cause when you put the kenwood into a sub-menu the only way to get out of it is to manually exit or when the radio power cycles it puts you back at the stand by menu)
10. took radio out and hooked up directly to car battery. when car is off radio doesn't power cycle but when I start the car with in the first few minutes the radio starts power cycling.
11. hooked radio up in my cousins 94 integra, radio never power cycled.
12. took steering colum apart and checked voltage at the electrical portion of the ignition switch as the radio would power cycle, not spikes or drops that were abnormal.
I do have two amps and an aftermarket viper alarm installed in the car. The alarm is not set up for starter kill. but I do have remote start setup even though I have a manual transmission. I have gotten so frustrated that I have hooked the radio up to the stock harness on my floor board(only ground, 12v constant, acc 12v are hooked up) and the radio still power cycles at random. Amps are not hooked up for power right now and radio is still power cycling at random happens when I drive or am just sitting in the garage with the motor at idle. I have hooked up a multimeter at the battery and with nothing on just at idle I get 14.4v, with radio and headlights on and my square fog lights depo brand no a/c 13.5-14.01v. with a/c on and everything else drops as low as 12.33v then jumps back up to 13.5-.8 when the a/c cycles on and off. At the constant wire car off I get 12.5 with car on get 14.4 depending what is on. I have monitored the the 12v constant with the car running and watching to see if there is a drop or spike before the radio power cycles but don't see anything out of the norm. Radio just seems to randomly power cycle.
My car isn't listed on the intake manifold wire harness service bulletin and the fuse #15 has not blown. there are no other electrical issues except the radio randomly power cycling.
Some help would be greatly appreciated I think I have listed all the things I have tried.