Why will my Mazda RX-7 Die out when the Alternator and all wiring indicate they are getting power?

[Jessica]

I have a 1986 non-turbo Mazda RX-7; twice now I have had the car slowly loose all power as thought the vehicle were running solely on the battery and it was dieing out. Light dimmed, fuel pump started sputtering to feed the car and all interior light went out. Once dead that was it, it had to be towed home. Testing of the Alternator proved that it was operating perfectly, light tester showed that the black w/ white wire that connects to the back of the alternator would get power when the key was turned on and the white w/ black wire shows that there is power to the charge indicator in the dash; also that the solid black wire on the left back side of the alternator is getting power as well. Lastly the 80A fuse in the main fuse box on the left side under the hood is still good. What else would be causing the car to drain itself and not replenish if everything seems to be getting power. This is my daily driver as running my pathfinder is way to expensive with gas prices.