If you're seeing 503 Service Unavailable errors, this means PHP processes are crashing while executing a script. As a result, Apache is not getting a valid response from PHP and considers the PHP-FPM service to be unavailable.
The most common cause of this problem is buggy PHP code, such as buggy WordPress plugins or slow scripts. The best solution is to disable all WordPress plugins and check your app's PHP error log and PHP slow log.
This problem can also be caused by buggy third-party PHP extensions or your server running out of memory.
For more information on resolving this error, see the article on fixing the 'Failed to read FastCGI header' Apache error.