What this sounds like is you have a "bad" new alternator. I'm guessing you bought the reman one cause it was a few bucks cheaper, keep in mind that the reman one went bad once before. I think if you swap out the alternator with a new one your problem will go away.
One thing to consider would be the connections to and from your alternator.
You might have some corrosion at the battery terminals or even inside the cables themsleves. At times there may be a good connections and other times you may have a bad connection.