Your fescue lawn can go brown for a number of reasons. Assuming it is brown during the growing season, when it is actually meant to be green, there are several common causes. Fungi can cause browning in patches or drifts, as can lack of sufficient water. Browning can also be caused by over-use of fertilizer and subsequent burn. It can also be brought on by scalping the lawn--mowing it too short for the species preference or mowing too short too quickly, causing a combination shock and sun burn.
Rhizoctonia Solani Fungus
Treat fungus patches on your lawn by altering your watering patterns and timing. You want to limit the amount of time the blades remain wet, so refrain from watering in the afternoon and evening or pre-dawn hours. Morning watering when the sun has come up is preferred and will limit the spread of the fungus. If the lawn looks parched but the soil and thatch is constantly moist, this is a likely problem. In addition to limiting watering, temporarily refrain from fertilizing the brown lawn; this is thought to exacerbate the fungus problem. Lawn fungicides can slow the spread, and new grass shoots will grow where the others have died, but excess moisture and ambient humidity are the two things you are battling.
Fescue can brown easily with a lack of or too infrequent irrigation. Most fescue grasses require a minimum of 8/10ths of an inch of water per week applied in one deep watering session or two shorter sessions. Warmer and/or arid climates or fast draining planting soils will require more water more frequently, and in very wet rainy or humid climes, slightly less watering is needed. Don't let the thatch and top half-inch of soil dry out between waterings.
Increase Mowing Height
Removing too much--more than one third to one half of the lawn blade height--in one mowing session will scalp the lawn and lead to browning. This is caused by a combination of drought stress, abrupt change in nutrient production via photosynthesis in the blades and burn from the sun. Refrain from mowing again until the lawn recovers some green growth and reaches 2 1/2 to 3 inches and then bring the blade height down to between 2 and 2 1/2 inches but no shorter.