For some strange reason, my random banner image was not being refreshed. Indeed the first time my blog was fired up in the browser, the banner would be random, but after that every refresh displayed the same image. As it turns out, it was necessary to include the following headers in my HTTP response.
Cache-Control: max-age=0, no-cache, no-store, must-revalidate Pragma: no-cache Expires: Wed, 11 Jan 1984 05:00:00 GMT
Pretty simple, don't you think?