We had a huge leylandii hedge in our last property and some sections of that had started to die. We were told it was a virus and there were some treatments. Since we were moving, however, we did nothing about it. It might be worth asking advice in your local garden centre.

Sometimes though, if the hedge has been cut back too hard, it will die off.

Take a close and thorough look at the good growth and check for aphids. If you see them that's the cause.

Smallish patches low to ground? could be dog or cat pee.

Could also be wind burn, in which case it shouldn't get any worse when the winds are over (if they ever are...)
Google confiers brown patches - there's quite a lot of info out there.