It is likely due to this issue: Contact Form 1.9.4 and later refers your upload folder setting in Settings > Miscellaneous menu for resolving the base directory for CAPTCHA’s temporary folder. So it may not use wp-contents/uploads/wpcf7_captcha. For example, when your upload folder is set “wp-content/myfiles”, CAPTCHA temp files will be created in wp-content/myfiles/wpcf7_captcha, so you need to make that folder writable.
The folder location is set under settings > miscellaneous
Most ftp programs will allow you to set folder permissions 777 will work, though others may suggest a more restrictive setting.
After making this adjustment mine works, you can see here:
Plane Charter