@arekkocowicz: I have the exact same problem with my Mini cooper and a new head unit (Kenwood). I don't have a good oscilloscope to check the voltage drop from my battery, so just for testing purpose I connected the yellow +12v constant cable from my radio to a stabilized power supply, with the ground attached to the chassis of the car. and as you guessed when I start the engine the radio didn't turn off anymore.
so I need to create the same circuit as you did.
Did you made improvement to your circuit?
could you provide a list of the parts you used with their respective values?
I know you used Su'scon 5.5F 2.5V x6 for the capacitors, but what about the diodes and fuse?
and where did you bye the Su'scon capacitor?
thanks for your help!