battery light keeps coming on

I have a 96 honda accord lx. 4 cylinder. and the battery light came on. we checked the charging system and the alternator was outputting too low. replaced and new one worked fine bt then after 50 miles the light came on again. took it back in checked it it was outputing 11.5. put another new one in light went off. after 20 miles the light came back on. what is the problem with my car? i had the battery tested and it tested fine. i have a optima red top battery. and they tested the alternator and it now is puting out 11.7. when looking the car over and it is running the light is on but if you disconnect the plug that goes to the alternator the light goes off. do i have a bad ground somewhere or is that plug bad? please help me this is soooo frustrating and iv taken it to a few shops and no1 is any help.

Hello
The battery potential output @ idle should exceed 12 volts. I'm sorry, I dont know the specific numeration for i4 accord. I'm suspecting that there is an electrical draw robbing alternator's potential. If you have technical repair manual, then it is best to reffer your findings with specifics.
Cheers

I had the same problem in my 86 accord and after like 3 alternator from kragen, i finally got a good one. They wouldnt replace my bad one too cuz they said that it passed their test. I went to a friend who works at kragen and he replaced it and havent had a problem since.
I cant tell you if you have the same problem but i was going through the same thing as you, trying to pin point anything except that.
Good luck