Are the amps turning off when the head unit is off?
Disconnect the power wire to the amp, and put a multimeter inline with the power lead, while the head unit are car are off. This will measure the current that is being drawn by the amp when there really shouldn't be any. Use this method to track down where the power drain is coming from. If it's a lot of current, either something is keeping the amp on, or you have a bad power supply component. Either way, there is still a lot of troubleshooting that you can do to track this down. Finding the culprit and figuring out what you want to do to fix it are two different things. Mass produced amps are often more trouble than they're worth to get fixed, unless you can find a good repair shop or send it back to the factory for repair or replacement.
What are you doing when you "unplug the sound system"? What are you unplugging? Are you disconnecting power at the amps, pulling a maxi fuse or whatever, or removing the battery cable at the battery?