Alternator problems?

About a two weeks ago all the idiot lights on the dash started flickering on and off, then the radio started losing power. Finally last weekend it was having a hard time starting. It would start with no problems if it was sitting for several hours but if i were run it for awhile, stop and then try to start it up again, it would take a while to catch like the battery was dead. I assumed it was the alternator thinking that the battery was being drained after useage not leaving enough juice to start back up.
I bought a battery/alternator tester from Radio Shack which told me my battery was low and my altenator was fine. Replaced the battery and it ran fine for about 3-4 days. Now I am having the same problem again. After usage it is having trouble starting back up. I replaced the alternator 7 months ago, it was done by a auto shop and they used a 'rebuilt alternator', which probably means that it came from a junk yard.
Does this sound like the alternator is dying again or could it be something else?
Thanks

What sort of starter trouble is it? Does the car turn aggressively and not catch, or does it turn sluggishly? Sounds like the latter.

The alternator is my bet for the lights/radio deal, but the poor starting makes me wonder. My impulse is that some wiring is struggling or your starter is dying. The alternator really has very little if anything to do with starting the car; the starter is powered by your battery and your battery alone.

At first it starts right up, if i were to turn off the engine after it had been a running for awhile it will start real sluggishly. The condition is worsening every time I start the car as I imagine the battery is getting more and more drained.
Correct me if i'm wrong but i don't think it would be the starter because with a fresh battery it will start like new, it is only after a 3-4 days after installing a new battery that starting is bad.

Does it turn aggressively and not catch, or does it turn sluggishly?