Every one pretty much agrees that turf grass needs about 1 inch of water (that should soak in to a depth of about 6 inches) per week. What is debated is how to deliver that amount of water with some people absolutely sure that 15 to 20 minutes every day is as good as some length of time needed to deliver that 1 inch once a week.
Those of us that do not have in ground sprinkling systems and water each area only once per week have noticed that the roots of our grass go deeper into the soil then does the roots of similar lawns that get that 20 minutes every day, and where the turf is sprinkled every day I have seen more problems with "weeds" that normally only grow where the soil is moister than normal, things such as the sedges.
Do not simply rely on someones estimate of 20 minutes, or any other time frame, to run your sprinklers but instead measure how much water is delivered in what time frame. According to our local Department of Public Works engineer the water pressure on our local system drops considerably between 5:00 AM and 7:00 AM because a large percent of the people on the system are showering, shaving, cooking, etc. at that time of day. There is another fairly significant drop in system pressure between 5:00 PM and 7:00 PM although not as much as in the morning.

Thanks for the reply, but it did not answer my question. I realize I should water an inch, preferably once a week to encourage root growth. My problem is I have a roughly 300 square foot zone where, about 25% of it has pretty much just sand. So do I stick to infrequent watering in the zone at the expense of the sandy area, should I stick with frequent watering to keep the sandy area wet, or maybe a compromise? I'm leaning toward the infrequent watering with the hopes that compost and organic fertilizing will build up the organic matter enough, that along with adding a little dirt in the sandy areas will allow me to overseed if needed. Then hopefully this area will be much healthier next year.

Water it as long as you need to so that it can go about a week before needing water again. Are you seeing the grass wilt in the sandy areas? -or just the soil drying out?

The grass looks OK so far, just that it's really thin with some brown stuff. I think the main problem is lack of water. As the mid summer wore on, that area started getting a little brown, and even though I started watering some more it just didn't seem to be greening up. I ended up getting some bags of cow manure compost and putting it down in that area.

The soil I have is sand. Where I have been able to get almost enough organic matter into the soil it retains moisture better then the places that do not have sufficient levels of OM. However I water once, or less, per week long enough to saturate the soil down 4 to 6 inches or about 1 inch of water from the sprinklers, and with my pump that often is 3 to 4 hours in any one place depending on which sprinkler I use and whether wife is also doing laundry.
No one can give you a definitive answer to your question unless they have exactly the same soil and water delivery system that you have. Start by setting out straight sided cans and measure how long it takes for you to deliver that 1 inch of water, and then dig into the soil in that area to see how deep the water has penetrated, and after doing this several times you may have a good idea what you need to do.
While I know that a green lawn surrounding your house can reduce the summer temperatures around that same house by anbout 10 degrees I do not fixate on having a dark green lawn that looks like a carpet. While I know a nice neat and green lawn sets off the flower beds really nicely, I do not fixate on having a lush green carpet around the flower beds. The lush green lawns often held up as examples of what you should have are a marketing tool of the companies that are selling the poisons that are killing the planet we live on.