After some research I found, that the problem was related to smilies. Yes: smilies!
When setting up my new Joomla 3.x site I manually copied all entries from the old Joomla 2.5 installation to the new 3.x installation. Some of the copied entries contained smilies. Means: <img>-Tags like this:
Code: Select all
<img title="Smile" src="media/editors/tinymce/jscripts/tiny_mce/plugins/emotions/img/smiley-smile.gif" alt="Smile" border="0" />
After deleting all smilies from all entries the problem has gone!
I can't explain, what smilies have to do with captchas. And I cannot explain, why this problem appears only randomly. I may speculate that the broken link somehow affects captchas. But I have no idea.
Anyway. I hope this information helps others to avoid this pitfall.
(And maybe somewhen some guru may explain why ...)