Amps cutoff, head unit stays on

I have a 2001 Jeep Cherokee. I run 2 8 gauge power cables from the battery back to a distrubution block under the back seat. I then run 8 gauge power cable to each of 3 amps: Jensen KA 4400, MTX Thunder 280, and Alpine MRP-F240 . Also, I feed a relay from the distibution block triggered by the remote lead from my Sony head unit, which feeds all 3 amps as well. Here's my problem, whenever I turn the volume up or play a CD loud, the amps die out, but the head unit stays on. The voltage drops coming from the remote lead fed realy output below 12 Volts as I turn up the volume. I wasn't able to pinpoint the exact voltage the amps die out at because my neighbors are outside, and I dont want to play the music too loud (gotta be a good neighbor) ;)

Will installing a capacitor inline help prevent this from happening? If so, should I place it on the "input" side of my distribution block so all amps and remotes will be covered by it? And how big of a cap should I get?

More details on setup:
Jensen KA 440: 400W Peak into 4 channels
MTX Thunder 280: 280W Peak into 1 channel (bridged)
Alpine MRP-F240: 100W RMS into 2 channels (bridged)

I finally got the search engine working and read a few posts about capacitors on the forum. Since my system is really only about 540W RMS, would I really need to upgrade my alternator? I was hoping that using the capacitor would help when the demand was there for more power, since my system is more "casual", and I dont turn it up really loud for long periods of time. Thanks for the help.

a capacitor is not the answer, it will only further tax your electrical system. Are your lights dimming when you have your stereo truned up? As far as the amps cuttin out try this run 12 volts from your power cable to the remote turn on terminal on the amp. Now turn up the stereo if it doesn't cut out set up like this its your turn on lead. If it still cuts out problem is else where. Make sure you disconnect the remote turn on wire from the stereo to this amp also.

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If the relay is connected to the distribution block that feeds power to the amps, and the relay is putting out below 12 volts, then there's a good chance the amps are receiving less than 12 amps as well (since the power source is the same).  When you check this voltage, where are you connecting the negative probe on the multimeter to ground- at the amp(s) negative terminal(s)?  This is where you should be testing.  Is this less than 12 volts with the engine running as well?

Check the voltage at the battery terminals while the engine is running and no accessories on (stereo off, etc.).  Are you getting around 13.5 volts or better?  What about when you place a load on the system by turning on lights, stereo, etc.?  If the alternator seems fine, you should check the amp(s) ground as the culprit.  If you're not sure about the alternator, your local parts store should test it free of charge.

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My ex once told me I have a perfect face for radio.