Jeep dies out while running and idle.

Dies out while driving and while at idle. It is like the key was just turned off but still in ACC. I lose my gauges but still have power to the whole Jeep. It will turn over but will not start the warning lights on the dash are on including the key light. When I turn the key off the hazardous flash twice. So if I let it sit for a few minutes it will start right back up. When it is down I have hooked it to a scanner and it says no key found turn key on. They key is in fact in the on position when trying to run the test. After the system starts to work again there is no warning lights on the dash anymore so the scanner doesn't find any problems. The Jeep starts and runs fine until it happens again. The battery is brand new I replaced it with a yellow top optima. The volts are good from the alternator they are steady 13.95 to 14.10. I have an older G4 Cliffrod alarm system in it. The people I have talked to said it's the alarm system causing it to shut down. Thinking that is been stolen or something. I am not so sure that it's the alarm that's problem so please if anyone has any ideas. I am open to try just about whatever it takes to get this thing running.