If SFC - Like Button or SFC - Share Button is activated then the CAPTCHA image is being selected for a LIKE or SHARE image. This causes a new session that breaks the captcha cookie rendering the CAPTCHA unusable. Also the user will see an error when posting the form:
"Could not read CAPTCHA cookie."
This problem with Like and Share has been fixed by the SFC developer and I.
He has yet to release the new version for auto update but it is available for manual install.
Later on when 0.22 is released it will be available for auto update.
If you need the fix now, you can manually update the trunk version of SFC 0.21 by downloading the zip and replacing the files by FTP.
Fast and Secure Contact Form also needs to be updated to 2.6.3 or higher.