Could be a number of issues here. With a 503 error like this it's likely to be an issue with the server, so you can check the Issues Log for the server that Nintex is installed on, or the web server that your web application is residing on.

As the title suggests, it's most likely due to the server being unavailable. Make sure the services are running ok, and if you can do it without too much disruption try and IISReset.

Thank you for the very quick reply Ryan.

I will have a look into the logs and try an IIS Reset