Uhhh ... nginx doesn't run on Windows so you must mean you use a Windows workstation and the Nginx server (linux) reports a 503 ... temporairly unavailabe. That error is somewhat illusive ....
There could be some related errors in your nginx server error logs ... or php error logs. So check those.
Are you running autobackups? Anything that would cause server to be busy and not accept new connections.
Is your cron job/task running as it should ... every minute is current recommendation by Moodle HQ.
Would think the moodle is setup to use files for sessions and not database. Check that .... use files for sessions.
If you are using files for sessions double check owerships/permissions on moodledata/sessions directory.
Do you have any additional protections for your site whose rules might kickin from time to time ... mod_security?
'SoS', Ken