try and put a dmm on it when its doing it and get the voltage readings when its on and when its off.

 

For the most part alts. put out more amps at higher RPM's. This is not always the case, but it generally is.
What are is your amperage demand of your amps?
The NINe.1 has a MAX current draw of 130 amps by itself. Not sure about your 4 channel amp.
The amperage output of your factory alt. is from 80 to 110 amps, depending upon options. This means that your factory alt. can put out at most 110 amps depending upon current demand.
If, between your trucks electrical current demand and that of your amps, you have a current demand of over 110 amps things will start to shut down.
Some high output alts are a little on the pricey side. I am sure you can find one for a decent price.
http://www.nationsautoelectric.com/fad-alternator.html
http://www.strauto.com/250245.html

 

9 times out of 10, when I have had weird problems, it has been an grounding issue.

I read your posts quickly and didn't see if you had checked your ground wire from your 4 channel amp.

Is it grounded at the same spot as your bass amp?

If not, switch them and see if the problem moves.

 

here is another way to look at what fozzy is sayin, even tho prolly not ur issue. i copied this from kinetik. simple use the wattage rating of the amplifier you are using. If the amp is not one of quality use the fuses on the amps and put them into this equation A x 12.5 = W this will tell you the total wattage that amp should be able to make. then again add them all up and you know the total you need to support. Vehicle - DONT FORGET THE TRUCK! many times people will replace the factory with a new cell or battery because they are adding audio etc but then they dont even think about the vehicle. The vehicle is designed to work based on its factory alternator and battery alone it cannot make any more power than that. So how do you find out what you truck needs to function. Simple use this equation again Amperage of your alternator x 12.5 = wattage Now the end result add up the vehicle,and the amplifier wattage take that total and this