Hi, Matthew.
Do you have access to any of your server logs via FTP?
They are usually located in a folder called /logs in your webspace. There your should be able to find some sort of info what happened, when the plugin tried to send the form.
Usually it has to do with the wp_mail() function that might not work or not be accessible any more for some reason.
A faster check usually is possible directly in the WordPress backend. If you have an SMTP plugin (e.g. WP Mail SMTP ) installed, please make sure in the testing section of the plugin that sending a test-email does work.
If it doesn't work, please post the exat error message you receive and the current version number of your form-plugin here.
Regards, Karl