The problem may occur if you have installed and activated some caching plugin. If you have one, just try deactivate it and check Captcha plugin.
If you have no access to your Dashboard, it is necessary to deactivate plugin manually. Please complete the following steps:
1) Go to the your_wp_root/wp-content/plugins folder via FTP;
2) Find "captcha" folder and rename into "captcha1";
3) After you log into your dashboard, you can rename the folder back.