1996 Jeep Cherokee, replaced dead battery, generator light still comes on?

I have a 1996 Jeep Cherokee Sport (6 cylinder). We replaced the alternator a couple of years ago. Two weeks ago, it was left at an airport when my boyfriend flew out for a family emergency. He was rushed and forgot to turn the lights off. So, it sat for 5 days (probably 4 of those days with the battery dead). He was able to get a jump start and get home. I was able to run some errands but then it died on me. Got a jump start and got almost home when it died again; then my boyfriend came, gave it a jump start and got it the last mile home. We replaced the battery and it started right up. However, today, I went to run some errands and on the voltmeter, the meter was at the line just above the red (borderline low) and the generator light came on. It made me nervous, so I turned around. Is this still a battery issue or could the alternator (just a couple of years old) be going again? Any advice would be helpful!