The problem is with your charging system, meaning the battery, alternator, and all existent power loads on your vehicle such as interior lights, head lights, air conditioner, etc...
If this is correct, you can easily verify it by playing a song that you are familiar with, especially the bass lines, and noting when the power is lost to your subs and head unit. If the bass and head unit resets just as a hard bass note is about to play or it plays for a couple seconds, then indeed the problem lies in your charging system. What this means is that your car's battery and alternator cannot physically handle the extra load of your Kicker L7.
I recommend replacing the battery since it is the cheapest route. The best battery to replace it with would be an
Optima yellow top, as this is a dry cell battery and would give you the best results, but simply a new battery should help out quite a bit.
Make sure you fully charge the battery before trying out your subs again.
If the power still seems to be cutting out after replacing the battery, you might after to consider replacing the alternator, but that is usually a last ditch effort unless you are into competitions, because it can get rather expensive. You would have to search for high output alternators.
Hope this helps!