When your vehicle is running, your alternator is powering your amps. If your current draw from your amps is too much, your alternator cannot keep up.
What is the total RMS output from your system? Also, what size fuses are used for each of your amps?
I think someone else mentioned this, but you have to realize a stock alternator is not made to supply a high-powered audio system. You do have some current to play with, but the stock alternator is built to handle the current demands of the car without an added strain from a powerful audio system. If you're running 1500w total RMS, then you're basically looking at an additional 150 amps of current draw. That's not set in stone or anything, but should be fairly close.