Could be heat (does it have plenty of air round it?). Could be a stray speaker wire strand causing a short - check all the speaker connections to make sure the ends are neat. If those fail, could feasibly be a short inside a speaker, which can be a pain to diagnose. Otherwise is most likely an amp problem...

 

Its heating up and going into protect because you have it wired to 1 ohm final impedance and the MRP1000 is not 1 ohm stable. You need to wire it down to 4 ohm's.

 

Well if your worried about the amp straining for power during hard bass and you already have lights dimming, sounds like you may want to grab a capacitor.

 

caps are crap, upgrade your electrical and wire your sub up correctly (to 4 ohm) a duel 2 ohm sub can be wired either to 4 ohm or 1 ohm. did you change the wiring of the sub when you moved it to the rear?

 

Verify two things. First if you have a dual 2 ohm sub it can be wired in parallel to 1 ohm (not good for amp and will cause it's demise) or in series to 4 ohm (much better for amplifier). This is an easy mistake to make. The diagram shown above is the correct and safe method if your sub is indeed dual 2 ohm. Next you need to check the ground return resistance. If you have a sky high resistance on the ground return to the amp, which increases as current is drawn into the amp (read that as increasing the volume), it can manifest itself as excessive heat as well. A good solid ground is going to show a return resistance of under 1/2 ohm and as close to 0 as possible. (never once seen 0 though).

 

that heat sink does not do much. It relies on a small surface area contact. It is not normal that your amp cuts out like this. I don't think that the different location of the amp makes any difference, even a closed trunk still provides lots of air.
Are you sure your connection to your subs and the subs themselves are still ok? Maybe the VCs are shorting out? What if you try to drive your amp with a continuous 80 Hz tone. You can download something like TruRTA that has a tone generator and connect your headphone output to your amp. I am sure your smartphone has apps for this to.
Try to run your amp at high power and measure the voltage at the amp pos/neg. If its much less than 11-12 volts you may have an issue.