People have problems with rebuilt alternators probably because they don't investigate and repair what probably killed a large percentage of the poor things to begin with.... bad cables and loose and/or corroded connections. Not just making sure the various lugs are nice and shiny and properly tightened everywhere, but making sure the inside of the crimped ends arent full of crap and corrosion as well, which is really easy to miss if you don't go looking for it. Throw into the mix a bunch of weak grounds throughout the engine compartment and a battery that is probably a couple of years old and not in the best health to begin with, and its easy to see why so many rebuilds fail so quickly in older cars.
I had one crusty old mechanic tell me, and it stuck with me forever, "most alternators don't die a natural death, they get quietly murdered". No warranty on alternators unless the battery cables are replaced and if the battery is more than two years old or fails a load test it has to get replaced as well.
I can think of well over a dozen rebuilt alternators that I've installed since I started wrenching and using his philosophy, most of them of the less-than-stellar-reputation Autozone/O'reilly/Advance Auto variety, and have only replaced two of them under warranty...one had well over 100,000 miles on it, and the other was on a 90's Corolla where the alternator is right up against the exhaust manifold, and the power output was fine but the bearings were singing loudly.