There are a couple of possiblities here, assuming the replacement alternator checks out ok. Most common, the main feed wire from the back of the alternator to the battery has a problem. In many vehicles there is a fuseable link where the wire attaches to the large starter bolt. (Again, this is not every vehicle.) This could be burned. An easy way to check for this is using a test light, one that you clip to ground then probe a wire to light it up. Ground it, then (carefully so you don't short out the tool) touch the large wire connection at the back of the alternator (with the engine off.) Many Fords use a second large connector on the side of the alternator; two large, same-colored wires are your feed wires. If it doesn't light up, that's your problem. Find the wire break. If this isn't the problem (98% of the time it is), there is the remote possibility that the switched feed wire to the regulator is not getting power. Basically, this tells the regulator that the vehicle is on and it's time to charge. Not a common problem though.
Voltage Regulator?
Have the battery checked out. It may have a dead cell and not holding a charge,
Try the cables from your battery and alt. Sometimes these can corrode.
Inside the alternator
old myth, bad for alternator, dont do this..
Try changing the battery.
my 05' cavalier has a bad alternator problem its charging the battery a little bit then stops and the little power my battery has is drained by the end of the night. I replaced the alternator twice and the battery but still no difference.
If the light remains on then the system still isn't charging as it should. Check the plug on the alternator and also that the wires to the alt have a good connection.
It could be an alternator. Check with a mechanic if that is the issue.
you have a short where negative is touching the metal of the car or it is grounded inproperly
A light is on or a relay is stuck pulling power from the battery.
?ignition control module/pickup