thanks a lot for your answer. My next answer to them (if they say again it is a wordpress problem) will be:
A 503 error is a server error: https://www.checkupdown.com/status/E503.html It’s thrown when apache or httpd isn’t running and can’t serve html or run php.
Something is broken at GD where the MySQL server is probably running and providing the database functions to your WP site, but something is dropping out on the httpd server. It’s Stablehost problem.
I hope they get it fixed soon….
Nicole