While the JL 1000/1 amp isn't a huge power hungry beast like some kilowatt amps but if certain frequencies are hit for extended periods at high volume it can significantly pull the voltage down in a car system. Especially if it's not properly wired or has a weak battery or alternator. If the voltage drops below a certain level(most after-market units are around 9.5 volts) then the head unit will shut off. After the head unit shuts off the power stabilizes and it can turn back on again. A stiffening capacitor can help this situation but it's just a band aid. The Supras charging system wasn't designed for extra electronics. It doesn't have much over head. And running a 1000 watt amp, especially one of JL's quality will require a significant amount of extra power. Power the system wasn't designed to provide. This puts a tremendous load on your alternator. Even if you get a stiffening capacitor I don't think that your alternator will be long for this world running that kind of load. Also if your battery has been drained a couple of times, unless it's a deep cycle it is no longer healthy and it's ability to hold a charge is significantly reduced. This will just place even more of a strain on the alternator. My advice to you is unless you really feel you need that amp, move to something smaller. Your running a crap sub on a good amp. I would recommend running a better quality sub on a smaller good quality amp. You will be happier with the end product. But if your set on running that amp you will need to upgrade the charging system on the Supra to properly support it.