Usually the problem is water, or lack of it, at times. These plants like moist but well drained soil, which means, in a pot, they need regular watering, with the ability to drain freely at the bottom, not being contained by an outer tray or outer pot. They can go brownish when exposed to cold winds, particularly north east winds, but that doesn't sound like what you're describing. I'm afraid, once growth has died back, that area of the tree will not regrow, though growth may continue at the top and other, living parts.

How large a pot, Jglennie? Cypress need a fairly massive amount of soil to succeed in containers. With a sea breeze, I would expect to need containers at least 2 ft. wide and deep for long term success. Depending on where on the coast you garden, I would expect to need to water at least twice a week--in Portland--to every other day--on Malibu Beach. If Goldcrest Cypress could survive the summer where I live, I would expect to need to water twice a day.