There are 5 things that protection circuits on amps will detect.
1. Short circuit on the output
2. Low volts on the supply
3. Overvolts on the supply
4. Overheating power transistors.
5. Overdriving the input stage.
1. and 4. are easy to detect.
3. Is highly unlikely unless your alternator control has gone wrong. you would know anyway as bulbs would start popping.
2. and 4. are the most common cause.
Low voltage can be as a result of the battery being less than able to handle the cars electrics and the additional load of your loud music.
Check this by putting a meter across the battery terminals, with the engine at tick-over it should read 13.8 volts.
Now do the same check at the amps supply terminals. should be within 1-2 volts, depending on the cable run from the battery.
Turn on the system and check voltage drop.
(When you test the system dont crank it up, just run it at sensible levels with something other than drum and base, garage, grunge rock or any of that heavy base stuff)
Check the voltage at both the battery and the amps supply terminals again. If you get near 10 volts, the protection circuit will probably cut in.
Thats deliberate set to save your speakers having raw DC shoved down them.
You will need to look to your battery and wiring to correct this.
Maybe a new higher capacity battery (see if the diesel version of your car battery will fit) and maybe have the alternators output checked. You need a specialist to do this, a good auto-electrician if you can find one. Lucas or L.UK as they call themselves now will do this for you..
4. will show itself if you are overdriving the input side as in :-
5. Some head units will have as much as 3v output and a lot of amps wont handle this level in. so if your amp has an input adjustment, turn it right down and this may solve the problem. You wont get any more output by over-driving the input...just problems.
When you have established where the problem is, you can set up your system for the maximum it can achieve, NOT the maximum you need, if its not capable of any more QUIT where its working.
Its like expecting 200mph out of a 1.2 Clio. Nice, but you will never get there.