After a long investigation why a Captcha image wasn't being generated, I discovered that BlogEngine.NET has the session state disabled in web.config. I am generating a Captcha image via a webpage and storing the text string in a session variable. I chose to turn the session state back on as this is acceptible for my needs.
Search in web.config for:
enableSessionState="false"
and change it to
enableSessionState="true"
BlogEngine.NET
Captcha, BlogEngine.NET, Session State