1999 Chevy Suburban

My 1999 Chevy Suburban has, for the last few month, been experienceing intermittment electrial shut downs while driving.I.E, comple loss of power. Engine quits, no lights, no instrucments. Nada but then recovers in one or two seconds. However, it recenlty failed five time in a one hour period. I installed new battery thinking that perhaps I haqd a bad cell. The car started then shut down. At one point, the securtiy light (beneath the steering column) remained on and the light for the "Park" indicator liight was on but that was the only indication of power. I checked the battery terminal and fuses. All O.K. I used the "Re-Learn" procedure by placing teh key in the on position for about 5 minutes and the system apparently restored itself and the car started only to die when I tried to drive it. I only applied the re-learn procedure once.I did not know at the time that I needed to repeat it two more times. Wil applying the procedure three time fix it? For Good? Does teh battery in the key fob affect this situation?
Thank you,

Jack