After sitting for extended lengths of time (3 hours or more) my van won't start?

After sitting for extended lengths of time (3 hours or more) my van won't start. I'll get a clicking noise and it seems that the dash light flicker. I can jump it and get it to start without having to have the cables on for more than just a few seconds. As long as it's not been sitting for a long time it starts back up fine after having been shut off. I had the battery and alernator tested and the guy at the AutoZone told me they were both fine. We noticed that the van had a hard time starting in the winter (either really sluggish or not starting) and all the lights would be dim until it idled for a little while. The battery light would also come on during then too. The battery light has also come on since then but has not stayed on for long. Any Thoughts?