Answer: It's certainly possible that there's not enough top soil to keep the roots happy at the top of the slope; you can test this theory by digging out a shovelful of lawn and inspecting the roots. More likely, the water you apply runs off before it has a chance to percolate down and wet the entire root mass. You can overcome this by watering the top of the slope in short (5 minute) bursts, waiting 5 minutes between water applications. To get an idea of how often you need to repeat this, place several empty tuna or cat food cans on the lawn at the top of the slope and run your sprinkler for 5 minutes; wait 5 minutes and run it again. Repeat this process until you have one inch of water in the cans. Excess water will continue to run downhill, keeping the grass at the bottom of the slope green.
A permanent fix would be to level out the top of the slope, and set blocks or timbers to divide it from the rest of the slope. This would at least give you a green, level area.
Best wishes with your lawn!
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