Encountering 2013 error ("Lost connection to MySQL server...")

[SantaMufasa]

I have a nightly job that performs backups on my MySQL servers. There are three production MySQL instances on different machines. My backups have been running successfully for months (until now).

However, on last night's backups for one instance, a couple of database/schemas (appear to have) backed up successfully, but the larger schemas failed, as follows:
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Backup of schema dhunt was successful in 0 seconds
Backup of schema mysql was successful in 0 seconds
Backup of schema support_appl was successful in 0 seconds
Error: Backup of schema support_dict was not successful (1115 seconds):
mysqldump: Got error: 2013: Lost connection to MySQL server during query when retrieving data from server
Error: Backup of schema test was not successful (0 seconds):
mysqldump: Got error: 2002: Can't connect to local MySQL server through socket '/var/lib/mysql/mysql.sock' (2) when trying to connect
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I re-ran the backup cron job with the same results. Does anyone have any troubleshooting suggestions?

Mufasa
(aka Dave of Sandy, Utah, USA)
[I provide low-cost, remote Database Administration services: www.dasages.com]