We have "Big Red." I cut our stems back pretty late last year, but we did have green leaves year round. Some of the leaves die but there should be new ones. Not much help but bumping up your thread.

Pretty sure they are all supposed to be evergreen. They are rather sensitive to poor drainage and too much water, maybe you should check your soil and water levels.

They also can get mealy bug near the crown down in the leaves that can make the leaves go brown eventually. Check for that too.

San Marcos website has a really good page on Anigozanthos care--its well worth reading.