Car Stereo System randomly turns on and off

I need some help. I have a 97 Merc. Mountaineer and up until a couple months ago, my system was doing fine. 800w Pioneer amp with two 12's in the back and a Panasonic Mp3 head unit. It just started randomly turning on and off and I have no idea what the problem is. Is it loose wires? Too much power? I know its not a blown fuse because the system comes on sometimes and if it turns off...sometimes, I can trigger it by turning on the headlights. Can someone please let me know what's going on.

tough to say. In my experience if something stops working after working properly for some time it can often be connections that have worked loose. If it is loose then turning on the headlights may draw too much current away from the already weak connection.
Again hard to tell with intermiten problems without checking the car. You can check the voltage and amperage that is reaching the power wire with a multimeter, try with headlights off and on to see if this is the culprit.

Sounds like you have a low voltage problem...you are probably getting low voltage due to the large amp and current draw from lights and such..check your voltage and see what you get..should be 13.8 to 14.4 at idle..If you can hook up the volt meter and drive around, see what the voltage is when the radio dies..you could have a weak battery or alternator problem that is just starting to show up..
If the charging system is ok then i would look into getting a cap or a dual battery charging system, or have the alternator "built" up to produce more amperage. 120 amps would do fine. An 800 watt peak from the amp is going to draw about 96 amps... 400 watts rms is 48 amps...most alternators only put out between 65 and 90 amps.. Stopping the voltage from dropping should remedt your problem...But like the prevoius post said, check your connections first. You could have a bad ground causing your problem.

as everyone else has said, recheck all of your ground and power connections

Sounds like you have a low voltage problem...you are probably getting low voltage due to the large amp and current draw from lights and such..check your voltage and see what you get..should be 13.8 to 14.4 at idle..If you can hook up the volt meter and drive around, see what the voltage is when the radio dies..you could have a weak battery or alternator problem that is just starting to show up..
If the charging system is ok then i would look into getting a cap or a dual battery charging system, or have the alternator "built" up to produce more amperage. 120 amps would do fine. An 800 watt peak from the amp is going to draw about 96 amps... 400 watts rms is 48 amps...most alternators only put out between 65 and 90 amps.. Stopping the voltage from dropping should remedt your problem...But like the prevoius post said, check your connections first. You could have a bad ground causing your problem.
Not sure how you are getting these amperage draw figures because 800 watts divided by a nominal 13.8 volts is about 58 amps max, this also does not account for efficiency of the amp and also that under normal usage--medium to low constant volume--average power would be only 10-20% of max power thus drawing between 6 and 12 amps (it looks like you used 8 volts to get your numbers). If amps drew the current you speak of then most cars would have their alternators fail in the long run, something that really does not occur.
Dual batteries are generally not a good solution for daily drivers because they create and extra load for the alternator to charge the battery. An upgraded alternator is always the best solution for a daily driver with excessive current demands. An 800 watt system in an SUV would best be supplemented with a 1 Farad cap.

My personal thought is, how old is your battery? It may be on it's last bit of life. You can get an optima yellow top on ebay for about 130 shipped.