My mobius camera is connected to the accessories wire and during ignition this circuit is open, so I had a similar problem as OP.
I made using 7 supercapacitors of 5F and 2.7V a circuit similar with a UPS power supply unit.
Also I made my own 12V to 5V circuit using a LM2576 regulator.
The result is an circuit like on attached image.
The final circuit (the supercapacitors and the 5V one) offer power for about 1 minute and 20... 30 seconds, is enough to start a normal car engine.
I uploaded more images on my Picasa account,
here.
I hope this will be helpful for others.
Later edit
I forgot to mention, when I wrote this message, the capacitors are loaded instantly when the accessories (in my case) are power on.
I'm not an electronics guru, so I'm very sure the supercaps buffer could be improved.
My first attempt wast to use the suppercaps buffer in the front of a normal USB cigaret charger and the time obtained was about 1 minute and 30... 50 seconds. I know, was a better choice
but once I made the whole power circuit I let it on the place.
So is your choice which one is better.