Almost always, the problem when lawns fail to grow on hills is lack of water penetration into the soil. The water runs downhill before it can soak in. The cure for this, if you have an in-ground sprinkler system with a timer, is to increase the frequency of irrigation and decrease the run times. In other words, instead of (for example) watering three times a week for 20 minutes each time, water six times a week for 10 minutes each time, or even more often if necessary. Keep adjusting the times until you see a difference. You’ll have to poke around a little to see if the ground is getting moist several inches down. Also, it would help to aerate your lawn with a core aerator to ensure that the soil is loose and that compaction isn’t contributing to the problem.