Its been going on for some time now - and there doesn't seem to be a solution yet.
From what I can see, several CAPTCHA images are being generated each time e.g. 1387403326.png and 991822372.png
but the image url in the form is *****/wp-content/uploads/wpcf7_captcha/692086990.png
But that image is either not getting generated, or it's deleted (no idea which)
Those are files and URL is 404 record.
Visually - I'm seeing the image get displayed, then almost immediately roll over to a new image, and roll over again to another image or a broken image link...
There's no clue to the reason in the WordPress or server error logs.
The same problem exists on testing site with only CF 7 and Really Simple CAPTCHA installed and active, using default theme. Occurs with WP 3.6.1 and 3.6, but no problems with WP 3.5.1 and earlier - didn't test with 3.5.2
I can't see anything in the plugin code to account for this behaviour - possibly it's a CF 7 issue instead.
Don't know if this info will help the developer.....