Check the three ways of the wiring harness between the alternator, the battery, and the vehicle. If the alternator has been replaced before, there will be crimps that attach the wiring together.
For unknown reasons, the instructions say to NOT solder the connections. On my vehicle, about two years after I replaced the alternator, I had similar issues. It turned out that the NON soldered connections had corroded. I simply soldered the connections and everything was fine, and has been fine for the last six years.
--Mark
http://www.marksatterfield.com