and i think the reason it doesnt cut out as much when the engines running is because the alt is charging your battery while your amp is pulling energy from the battery, meaning when its off your amp isnt getting enough energy causing it to cut out more. if you had a really good electrical system it probably would run fine. again, not to sure, just going by what i try to learn on here.
tell us the model number of the sub and we can find out more of whats going on. pics to if you can.
edit: heres info on your amp
Specifications supplied from Kenwood:
-Power MOSFET switching power supply
-TRI-MODE™ speaker operation
-Gold plated power and speaker terminals
-Stereo and mono operation
-2 Ohm stable
-Power consumption (4 Ohms, 10% THD)..........43 amps
-Operating voltage................. 14.4 (11-16 allowable)
* Audio Section
-Max Power Output..800 Watts x 1
-Rated Power Output.....
Normal (4 Ohms)(20Hz - 20kHz, 0.08% THD.......150 Watts x 2
------ (4 Ohms)(DIN: 45324, +B = 14.4 volt....150 Watts x 2
------ (2 Ohms)(1kHz, 0.8% THD)...............230 Watts x 2
Bridged (4 Ohms)(1kHz, 0.8% THD)..............460 Watts x 1
Frequency Response (+0, -3db)................5 Hz - 50 kHz
Sensitivity (rated output)(MAXIMUM)..............0.2 volts
--------------------------(MINIMUM)..............5.0 volts
-Signal to noise ratio...............................100db
-Input impedance...............................10,000 Ohms
-Low pass filter freq.(18db/oct)........50-200Hz (variable)
-High pass filter freq.(12db/oct)........150Hz (selectable)
-Bass boost circuit (90Hz)...................OFF/+12db