I just changed the alternator in a 1991 Lincoln Continental, and when I put the belt back onto the alternator, it was loose. I checked it for damage, and it is fine. It appears that the tensioner pulley is also fine, and I haven't missed any pulleys as far as I can see. What could be the problem?
The routing of the belt can be tricky some times. Usually there is a diagram with the routing. It can be as simple as what point you go around the tensioner. Check your routing versus the diagram and see if it is correct.
If it is, then suspect the tensioner has gone bad. My money is on the routing.