I'd say check the following:
a) make sure the power cable to the amps from the battery are sufficient guage. Too small of a power cable over a long run will mean voltage drop and the amp will try to draw more current (amperage) to compensate or simply cut out in total.
b) make sure the alternator is putting out proper amperage. It may be the same as factory (130 amp) at a stated rpm, but the output drops as engine rpm drops. Get it load tested to make sure it is doing what it is supposed to do.
c) check the battery to make sure it is still good. I have a yellow top myself and they are good, but any battery that can't hold a charge puts that much more of a load on the alternator.
d) try things without the cap in the power stream. The cap is just another load that the alternator has to try to keep charged while providing power to everything else.
