I have read about this, and honestly the installer did nothing wrong.
It's the newer vehicles that have the automatic engine stop/start (instead of idling). What's happening is just like when you start your vehicle, you are losing power to all accessories when it cranks.
The problem is that you don't want to have any other draw when you are using the starter.
So your head unit has two "power" wires. It has a main 12v feed that supplies power to it, and there is an accessory wire that acts as a switch/a power button. When you turn the key back, or are running then your accessories are switched on.
If you have a system with amplifiers, you are going to create a big draw on your electrical system when starting. To the point where you might be cranking for a while, might not start when it's cold, and will be causing more wear on your engine.
I know in some GM vehicles, that stop/start has believed to cause a lot of upper engine issues. On the v8s that have this, the engine stops, and so does your oil pump. The oil drains back into the pain, then the light turns green, and you hit the gas hard because traffic is taking off, and the oil hasn't yet circulated back into the top of the engine. There has become a known problem of lifter failure that this is believed to be the cause of. Some people have turned this off because of stereos and this issue. - might be a consideration.
If you don't have any amplifiers, I believe you can solve this using a relay and some other switch that will more or less prevent the head unit from losing power for 10-15 seconds, which should be enough time to regain power.
If you have amplifiers, then this is where you would want to consider adding a battery isolator and a second battery. The second battery would keep this going, and would not be controlled by the engine.
If you were dead set on the cheapest and easiest way to solve this, you would take those two "power" wires, and just wire them both up to the main 12v battery feed. The problem is that it would ALWAYS be powered. You would want to wire in a manual switch (button, toggle, etc), inline for that switch wire. IF YOU FORGET ABOUT IT, it will drain you battery and eventually kill it.
I had to search what a Ford Ka is. That's a pretty small vehicle, so you probably don't want a second battery, and probably don't have large powered subs.
The only question I see is are you saying it didn't do this before? Not until the new head unit? I thought the vehicles that had this feature, had this problem. I find it real hard to believe that any professional installer would use different wires then what was there and already installed. It would mean they would have to find and use a different switch wire.
(just brainstorming, perhaps the factory head unit had some sort of battery that prevents it from losing power, like a mini capacitor that is designed for that power cut). If you have that head unit you could just put black to battery negative, and take those two wires and connect em to battery positive for 30 seconds. Disconnect battery positive and see if it stays on for 2 seconds or more than 10.