Have the water tested, there may be something in the water supply causing this in your area. I have a well and get that same thing, but I know why I get it. I have a main filter that eliminates the odor, so when I smell it I know it is time to replace it. Most home centers carry a complete water test kit that checks for Iron, hardness, chemicals, bacteria, and pesticides that you can do in hime, there is alos a kit that has a bottle and a mailing carton that you send your water sample out in that cost about $4.
I am guessing that the faucet it the furthest one from the main so the water has a chance to sit in the pipe for a while and will take about 3 minutes to flush with fresh water. If there is a high iron or other bacteria count in the water supply, it only takes about 8 hours for the smell to build up. I have very high iron in my well, so I am speaking from experince. My iron content is around 18-20 PPM. I have 2 filters, on a dedicated iron filter that removes 15 PPM, and a water softner that removes 10 PPM. I know when I am low on salt just by the smell.