Самый простой способ обновления рисунка:
<img id=_captcha src="/includes/kcaptcha/?PHPSESSID=eee8e9ebeea5c116601fbd7036342e13">
<a href="./" onclick="document.getElementById('_captcha').src = '/includes/kcaptcha/?PHPSESSID=eee8e9ebeea5c116601fbd7036342e13&'+Math.random(99999999999999999); return false;">Refresh captcha</a>