I had the same issue. Mine was because I am on a Windows Server and had the captcha module installed. It was having issues deleting the files for the captcha and throwing a warning. Edit really-simple-captcha.php and anywhere you see unlink change it to @unlink. It should be around lines 190 & 215. There is actually a better fix to actually resolve the delete issue but this is a quick fix so messages can send again.
To fully resolve this issue, see: http://wordpress.org/support/topic/plugin-really-simple-captcha-function-cleanup-unlink-permission-denied?replies=14
If you do not fully resolve the issue, eventually your website will slow down drastically.