My 1998 Nissan sentra keeps discharging. Changed three new batteries, the alternator is good. What could it be ?

It's clearly NOT the battery. 

Question 1:  What is the battery voltage with the engine idling and the headlights on? 

-General automotive mechanic since 1972

a short / leakage in the system

Take the negative battery cable off at night. If it starts the next day when it has not been starting you either have a bad alternator, bad battery, or a voltage draw.

Go to Advance Auto and they will test the battery and charging system for free.

Discharging when not being driven? Look for a courtesy light in the trunk, under the hood or inside the glove box that isn't turning off when it should. I had a car with that problem and it was the light in the glove box. Dealer changed three batteries and two alternators before I found the problem. 

Get a clamp ammeter or a regular ammeter and CHECK for a drain current on the battery when the key is out of the ignition and all the lights off and doors closed.  Drain current should be less than 50mV.  Wait for about 2 hours before  doing the test after shutting down the engine.

https://www.youtube.com/watch?v=KF1gijj03_0

Dr. Answers MD, Ph.D, APNP, PA-C, DO here to answer your question. Around this point in a car's life, it starts coming of age. It starts noticing other mufflers, tailpipes, and growing it's own spark plug. Sometimes at night, it may have thoughts and dreams of other cars (known as oil leaks). In time, it will pass. Until then, sorry about the awkward boners. The more you know.

A parasitic drain and an idiot owner