Hi Joe,
I can remember, that with Visforms prior to Version 3.6 there were sometimes problems with the display of the captcha image. As far as I can remember there were two different reasons.
First the router does not work properly (for which reason so ever) and therefore the image was not found. I changed this in Visforms 3.6. The link to the image is no longer routed, but because Visforms 3.6 comes with lots of new features and many view files are changed, so that you have to recreate template overrides if you have made some, I don't know whether updating to Visforms 3.6.10 (you can download it in the downloads menu) is a good option for you. (Making Backups, Running the update, Checking if everything works still fine, may be a lot of work and it is not sure, that the captcha problem will be solved by this).
Second the captcha image can not be created (and is therefore not available). Visforms captchas use the popular php captcha script secureimage to create the captchas and this script sometimes (rarely) does not work. There is an faq on the autor website
www.phpcaptcha.org/faq
You could try to enable debugging on your website and turn all error messages on (Joomla! configuration) and look, if an error is thrown. Maybe, in addition with these faq's you can figure the source of the problem.
Alternatively you could try to use the google recaptcha instead of the Visforms captcha. This is a totally different technology and might work fine, even if the visforms captcha does not.
Regards,
Aicha