I tried adding open-files-limit=4096 in /etc/my.cnf and restart mysql. Then executed automysqlbackup again, this time got something else.

Errors reported during AutoMySQLBackup execution.. Backup failed
Error log below..
-- Warning: Skipping the data of table mysql.event. Specify the --events option explicitly.
mysqldump: Got error: 1142: SELECT,LOCK TABL command denied to user 'root'@'localhost' for table 'cond_instances' when using LOCK TABLES

Checking for fixes