This is a new issue happening since 2015-12-15 between 1PM and 7PM. There is an increase in traffic in serveral mysql servers, in particular parsercache and s4 (commons) servers, which leads to a higher amount of failed connections.
From the initial report:
Also happening about once every few minutes for parsercache servers
Last 3 hours in requests to /rpc/RunJobs.php on mediawiki-errors dashboard in logstash:12x Error connecting to 10.64.16.157: Can't connect to MySQL server on '10.64.16.157' (4) - pc1002 12x Error connecting to 10.64.16.156: Can't connect to MySQL server on '10.64.16.156' (4) - pc1001 11x Error connecting to 10.64.16.158: Can't connect to MySQL server on '10.64.16.158' (4) - pc1003