The first chimney I ever had (not a Weber) got left out in the weather a lot and only lasted a couple of years. My current one (a Weber) has been kept inside since I got it and is still going strong after 5 years. I also have a no name chimney that I got with a used kettle is still in very good condition. Sometimes I use both to get 2 kettles up and running.
Take care of your chimney and it'll last a long time.