Pics are nice, but we need to know a few specifics:
Quick observation: Since you are running a ported box, I'd engage the amp's Subsonic Filter to 25Hz (labeled as "ISF" with the 3-position switch on your amp). This might help as-is...
What voltage are you reading at the amp's +12/Ground terminals when the amp shuts off? Then, what voltage do you read at the battery when the amp shuts off (enters protection mode)? If both get close to 10V, then it's likely your battery and Alternator just can't cope with the ~60-80Amp constant draw of a sine wave (rap bass / 808

). You could also check the battery ground to make sure it's solid and of acceptable gauge (I'd say battery ground should be no smaller than 6Ga).
If the Battery reads around +12V but the amp drops close to +10V, then the connections from Battery to Amp, and Amp to Ground need to be inspected as they are likely terminated improperly (high resistance terminations = Voltage Drop). Inadequate wire gauge is also a culprit in this scenario - but your 4Ga should be sufficient.
I doubt this is an alternator issue as my stock 150Amp gladly handles my 3600 Watt RMS system with a larger 31M battery under the hood (and that's a "True" 3600 Watts, not "Peak Power" :bolt: ).
I honestly believe the amp is just not up to snuff for your expectations and desired listening habits @ 2 Ohms.
You can also try running one sub at a time (try both, but separately). If one of the subs is flaking out (shorted coil, etc), it will likely still trip the amp's protection even if running by itself.
Lastly - If you want to try another test - connect the two subs in series, and see if the amp still has problems. Since you have both sub's wires ran to the amp, it is simple:
Disconnect one sub's "+" and the other sub's "-" from the amp's terminals, and connect them together (leaving the remaining wires connected to the amp). This is a quick way to run the subs in series and end up with an 8 Ohm load to the amp. The amp will put out less power at 8 Ohms, but is not likely to hit it's protection circuit and will run more efficiently and stay cooler.
If it runs w/o shutting off with the subs wired in series - I'd suspect the Amp just can't cope @ 2 Ohms and a heavy hand (assuming the voltage drop was not the initial issue)...
