if you're tapping into the cig port, it will cut off power when the car is off. I would advise against tapping into a constant power source since it will drain your battery and there is no discharge protection as far as I know. however, they do have a thing called the power magic pro that Blackvue makes which has the discharge protection you are looking for.
I have the mini 0806 and I just plugged the camera into the cig socket in the glove box and ran wires from there. we have two cig sockets anyways so I don't mind having one taken up.
also, update the firmware on your 0806. you can find updates at
http://mini0806.com/update.html . I believe there is still a glitch where the camera freezes up when it switches over to the secondary memory card after the first one fills up. I'm just using one 64gb card. make sure you format it to FAT32 and don't use the built in formatter on the 0806 as it will format your card wrong and issues with saving footage will arise. you will need to download a tool that can format in FAT32 since windows cannot do it for anything over 32gb.