A 503 "Service Unavailable" HTTP Status code is a type of server error that may be returned when trying to access a page or other resource. Visitors and search engines will not be able to view the content on this page when receiving a 503.
This message is usually seen when the server is temporarily down due to overload, system maintenance, or another temporary issue. When a search engine encounters a 503 error, they will typically view it as a temporary issue and not immediately remove the URL from their index. Instead, they will allow the site some time to recover and return in a few hours or days.
As long as the issue is resolved relatively quickly, it's possible these pages could suffer a short-term rankings problem, but will general come back quickly after the site is back up. However, if the problem persists for more than a short period of time, it's possible search engines will begin to remove the URL from their index.