You also might be interested in this page that discusses the wild ancestor of the modern bell pepper. There, it says that it (Capsicum annuum) in its native habitat starts out as herbaceous but does become woody and shrub-like. A short-lived perennial, it usually lasts about 3 to 4 years.
Bell peppers are tender herbaceous perennials usually grown as annuals in non-tropical conditions. They might last a few years, but they turn woody.
Here is one person's experience with the longevity of various pepper plants:
http://www.homegrown-peppers.com/growing-peppers/how-long-do-pepper-plants-live/
You also might be interested in this page that discusses the wild ancestor of the modern bell pepper. There, it says that it (Capsicum annuum) in its native habitat starts out as herbaceous but does become woody and shrub-like. A short-lived perennial, it usually lasts about 3 to 4 years.
http://www.fs.fed.us/global/iitf/pdf/shrubs/Capsicum%20annuum.pdf