IIRC those subs are only RMS 250 watts or so. Ergo, do NOT listen to the poorly written answer that recommended a 2000w amp. You need to get an amp that is RMS 500w and you'll be better off. For example, an Alpine MRP-M500 is a mono amp that runs at 500w at 2 ohms.
I don't know what the ohms are on those subs you've got, they're probably dual voice coil; if they're dual 2 ohms, you can wire the DVC in series to make each sub 4ohm then wire the two subs together in parallel to get a total impedance of 2 ohms.
Your protection mode is more than likely a symptom of a bad amp or a bad install. You could have too small of wire for the power or ground wires for the amp, you could have a bad ground connection, or the amp could be getting too hot. Conversely, if you're running your subs at too low an impedance for the amp, that would do it too. Say the amp was rated at 2 ohms and you have your subs wired to 1 ohm total impedance, that would cause problems.
I have a MRP-M500 using 8 AWG power and ground and it's installed in a covered compartment and it has never gone into protection.
