2004 Honda Accord alternator issues

In the past 3 weeks I have replaced the alternator 3 times the first 2 were rebuilt the last one in a new honda alternator. Each time the alternator is replaced the battery light comes on. Before the last one was put in the car was parked for about a week with out being used and the battery was completely dead. Today I had the brand new alternator put in - my mechanic tested to make sure it was not draining and driving home about 3 miles from the shop the battery light came on again- What is going on! It was thought that the issue was that it was not a brand new Honda part but that doesnt seem to be the case Help me please!