Digital Display

I just replaced my battery on my 78. Before I had to replace it I noticed that the digital clock display on my radio would be on when I would go to get in the car. It is also the original radio. After replacing the battery I've noticed the display doesn't come on after the ignition is turnded off. The battery was just 19 mo. old and was a Wal-Mart Everstart. I got a free replacement because it was less than 24 mo. old. I am wondering if it is just a cheap battery and to just keep replacing it for free if it goes bad before 24 mo. or if there is a short going to the radio.