Electrical problem in 1999 Civic

One evening I parked my car and 30 minutes later went to start it and everything was completely dead - nothing worked. I had the car jump-started and drove home. 24 hours later - it started right up as though nothing was wrong. The battery was only 3 months old, so I took it back to Walmart. On the way there the electrical system cut out for about a half-second, but the car kept running. The mechanic confirmed the battery was completely dead so they replaced it. However, the car still would not start. After about 20 minutes of trying to figure out the problem, it started. I took it to a repair facility telling them the problem and not to turn off the car. Well - of course they turned it off, but it started up right away and caused no problem on the way home (did not stay as they were closing). I was told that something is draining the battery, and it was probably the alternator. Honda say no (on phone) - did not sound like alternator problem and she had only seen one in 8 yrs go bad.