The "Service Unavailable" or "503 Error" message may appear for a couple of reasons. This error may occur if the site has been suspended in Plesk or if the application pool has crashed on a Windows hosting account using ASP.NET.
If the site is suspended it will show under the status section in your Plesk panel. This could occur if there is a billing issue or abuse.
If the site is active in Plesk it's likely that your ASP.NET application has crashed its pool. As a temporary fix you can click on the "Dedicated IIS Application Pool for Website" link within the Plesk panel of the site and click on the "stop" and then "start" button to reset your IIS application pool. You'll have to debug your code for a permanent fix.
