This is a hosting/server issue and means your Sendmail facility is not configured correctly.
Contact your web host and ask them why your server will not execute the Sendmail program. Shared hosts and default server configurations often disable this function for security reasons and to avoid spam issues.
If you were able to send emails using Sendmail before, ask them to fix it for you. Maybe an update was made that broke your server configuration, only your web host can confirm this. Checking your server logs should point you and your web host in the right direction.
While it is easy for web hosts to say that it is a problem with the script, the error indicates a "refusal" from the server (assuming Sendmail exists at the /usr/sbin location), not anything the software is doing wrong.
If your web host will not enable Sendmail, use your SMTP connection instead.