If you have a Fairy Ring(s) on your lawn, the way to solve it / them is to apply a wetting agent such as Lawn Quencher – Lawn Dry Patch Remedy to the complete circle, inside and out and about a metre diameter away from the outer edge to get the area wet again and sufficiently wet to then support new grass seed.
The little natural micro organisms and bacteria in your soil that usually munch away at the thatch and fibre of the lawn produce a waxy waste substance that will coat the soil particles of the soil to make them hydrophobic and repel water. This is why the grass dies.
Watering daily with a Lawn Quencher – Wetting Agent Tablet will break the crust on the surface of the lawn by placing the tablet in a hose feeder / diluter. Apply daily for the first week, then once a week and then once a month.
See how the ‘softened’ water penetrates the crust instead of running off by cutting into the crust with a sturdy gardening penknife. It will take a while to cure the problem but then you will be able to locally aerate the problem area and over seed with fresh grass seed. Keep up with the application regime as a preventative measure. Keep inspecting with your gardening knife as time progresses until the soil remains moist to a depth.