Appx. three yr old gas hot water heater had no heat, so I relit pilot, observed burner turn on, went about life. Somehow both burner and pilot went out again. On suggestion of Home Depot genius, I replaced the entire burner/pilot control unit. New unit got a good pilot, then burner. Worked fine for a week. Now, pilot and burner are both going out again. Note: Did not replace pilot tube assembly or lead to single use overheat trip. Pilot does light after cool-down, and burner does come on, and can be manually shut down by turning to vacation, then brought back up. Seems to only happen when it's left on for a good while. Then the whole thing just shuts down.

My kitchen sink and 1/2 bath are a long run from the hot water heater. As such it takes a long time for the hot water to come out hot. I understand there is some type of a circulation system available. What is it, where does one get one, does it work, can a DIYer do it? What would it do to my gas bill?