My latest battery charger has a maintenance mode (?) where it runs the battery down, then recharges it. I have used it a few times on cars that have sat through the winter and not had the battery removed, stored indoors and put on a battery tender for the 3-4 months. it sometimes works, and sometimes doesn't.

 

In my experience, faulty remans alternators seem to be common. When my alternator was whining, I changed it out, twice, with remans due to low charging voltage. I got fed up and bought a brand new OEM unit and problems went away.

 

That was also Land Rover's experience as well a few years back - their reman's were giving out before the LR warranty period expired, (very bad), and hence LR was having to regularly install free replacements - really bad. As such LR quit making reman's available and only sold new manufacture.
I also had a reman fail - it was not so much the alternator as the built in "smart regulator" which in my opinion is very "dumb" as it takes its instructions from the engine computer, not battery state.