Go buy a Digital Multi Meter. You cannot troubleshoot without the proper tools.... Walmart has them for $10-$20 bucks. Its a wise investment trust me.
You can do 2 things right off the bat...
1. Check your battery voltage, secondary battery (if there is one), and amplifier voltage. Check the amp before it shuts off, and right during/after if possible. This can tell you if your voltage is dropping and your amp is shutting off because of it....
2. Test the Ohm of your subs. You do not have to pull the subs out of the box to do this initially. Take the speaker wire out of your amp, and hook it up to the Digital Multi Meter. Make sure you set the meter to Ohms... It will tell you as an example 1.0 , 2.0 , 4.0 or even something crazy like 1.33 or something like that. That will tell you that you are plugging that ohm load into your amp....make sure its not below your recommended ohm rating.
Those 2 things are crucial man....seriously. For $20 bucks to know that info is beyond worth it. If your lucky..maybe even Auto Zone would be nice enough to test your battery voltage.....if the guy is cool ask him to check your amp voltage, lol
As a side note...its not the best way, but it is better then by ear. The digital multi meter can help you set your gains on the amp also. Google how to do it. Basically you get a 0 dB test tone of whatever Hz you are looking for. Unplug your speakers, and turn up the volume on the HU to about 75-80%. Plug the DMM into the speaker terminals. Their are spreadsheets that tell you for this wattage, you adjust the gain to this....or that. Like I said..not always the best way, but another good thing a DMM can do in a pinch if you dont have a scope to check for clipping.