It's perfectly normal for some canes to die each season, but it doesn't look like the plant is dying to me, because you also have healthy green canes. So as Jeri said, remove the dead brown canes (this is normal maintenance of a rose bush). Then give the plant some liquid fertilizer, and you can expect to see new canes grow over time.
Edited to add: I made my post at the same time as Ken, and it's interesting to note that we are all offering similar advice.