Electrical not working properly

Driving along and notice battery warning light illuminated at stop light. Rev car up a little and light went off. Pulled into parking lot. Checked belt. Everything looked good. Decided to try and get home. Drove approx. 4 miles. Battery light off at first when rpm's above 1,200. At 45 mph the battery light and almost all other warning indicator lights came. Not the check engine light. Gauges quit working, dash lights started flashing. Car went into limp mode. Drove for about 1/2 mile to find place to get off of road. Check engine light finally came on. Turned car off. Checked under hood again. Everything looked good. No odors or anything. Went to restart and it just clicked. Had it towed home. Got up the next morning and put the battery charger on it. Went to work. When I got home 6 hours later battery was charged up. Disconnected charger and started car. Warning indicator lights still on and gauges not working. Put volt meter on battery while running 12.3v. Turned vehicle off. Put code reader on vehicle. The only code was a low voltage code. Battery is new and battery connections looked clean. Alternator new also. Decided to clean terminals anyway. When done started car and all is well. All gauges working and all warning lights off. Charging at 14.4v.
Drove car for a little over a week and all warning lights came on again. This was at start up at a restaurant after being off for approximately 30 minutes. Disconnected negative cable for 5 minutes reconnected all is well and car runs and operates perfectly. What could this possibly be? Something is resetting when battery is disconnected.