I don't believe any hair on the human body truly grows continuously. Even head hair has a lifespan of ~7 years and whatever you can grow in that time is the max. I was a big metalhead in high school and grew my hair out. Indeed, after about 7-8 years it stopped getting longer, right at about waist level, and was stuck there until I finally got sick of it and cut it off.
I think they call this the "terminal length". As long as it will grow before it falls out.