Stick to your guns on this one. 6 is too young.
I leave my older two alone sometimes. Here are my considerations;
-How far is the parent going?
-Can the parent be reached at all times? (I have Bluetooth in the car and recommend it for this reason).
-Does the child know how to reach the parent?
-Is the child good about answering the phone?
-Will the child not go to the door or look out the window if someone comes to the door? (tough one)
-What is the housing situation? Apartment with at-home neighbor? Cul-de-sac? Single family home with bushes hiding it from the street and access to the road from two sides? I just described the perfect house to rob.
At age 12, a totally reasonable age to leave a child at sunset, someone tried to break into our home while I was alone. I screamed, hid in the yard and ran to the neighbors'. They left quickly.
Let me add to that story that it wasn't the only time. If you or a neighbor have been robbed in the last few years, you should put off leaving your child alone for a long time. If someone sees you pull out of your driveway, that is usually the opportune moment, as what happened in our case.
Our house had previously been targeted, right after we all left for dinner elsewhere. When they tried to get in, my parents had just left. They weren't concerned doing so because my sister was supposed to be dropped off. So I didn't think much when a car pulled up, thinking it was my sister but then thought it odd that she didn't come in right away. I came up to the door and could see the knob jiggling and could hear something metal being placed on it. The last time we were robbed, they had gotten in by using a metal device on the doorknob to force it open. I put it together quickly that the same guys were in process of returning (common, new stuff replaced by insurance).
The first time, the police came and told us right away, most who come to rob, that is their intent. Criminals tend to stick to their speciality. So, I was told, usually if they get wind that someone is home, they will abandon the project immediately.
Usually the horror stories of being robbed and then killed are when the criminal is caught, cornered, etc. It's not very often than they go to take valuables, hear a child inside and say "Oh, let's kidnap instead!" So I took comfort in the fact that I really didn't risk being raped or killed. These were (drug addict) robbers who wanted money for their next fix.
The police told me that if I heard a sound, to simply yell at the dog. We don't have a dog so a better solution is to call the parent and talk loudly. The dog solution was also in the days before cell phones. If your child hears anything, instruct your child to do one of the above. Make noise and make it obvious that they are there.
Don't make the mistake of tracking the crime rate in your neighborhood. We were in a very nice suburb in the S.F. Bay Area. The dodgy area was a good 40-45 minutes away. They commute.
If I leave mine, I just make sure that I can get back quickly. For example, I swim but wont do it leaving kids alone. Can't get a hold of me in the pool! I will go to the grocery store. You may or may not be able to leave quickly from work. I also wont leave the two younger girls alone, although I will leave the two older ones. The two girls fight.
This might be a good regular baby-sitting assignment for a teenager. A six year old doesn't need the care and supervision that a younger baby would so perhaps a local girl would like to help out for a reasonable fee. Another solution would be to have him go to a friends'. Again, a SAHM might appreciate a bit of extra cash for doing what she usually does anyway, be home with her kids in the afternoon.