cva-1003 volume?

Are you running your mids/tweets off the built-in amps?  Realize the amps in the Alpine are rated at 4 ohms and are not 2-ohm stable.  It sounds to me like yes, the system is going into protection, so do you perhaps have a 2-ohm load on the amps?

The specs on the Alpine are only 19 watts RMS (45 watts peak) into four channels at f ohms with a 14.4V power supply.  This is not going to "play loud" if that's what you are after, and you may need an aftermarket amp.

Like I said, it depends on how they are wired.  If they are putting a 2-ohm load on the CVA-1003, then that is the problem.

Do you have your "mids/tweets" wired in parallel to, say, the front channel outputs from the Alpine?  Are you using a passive crossover?  Did the crossover come with the speakers?  What kind of speakers are they?

Try measuring the ohms of the speakers at the radio to see if they are running a load smaller than 4ohms.  If the speakers are running in four ohms you might want to disconnect all of your speakers and hook them up and test them separately.  If the system cuts out when hooked up to a certain set of speakers you have narrowed down your problem.  Once you locate what set of speakers are making the system cut off you might want to remove the speakers and test them.  From here you can find out if you need new speakers or if there is a wiring issue.