解決策の考え方は明らかです。現在の接続が切断された場合は、mysqlに再接続してください。
これをチェックしてください:
def make_sure_mysql_usable():
from django.db import connection, connections
# mysql is lazily connected to in django.
# connection.connection is None means
# you have not connected to mysql before
if connection.connection and not connection.is_usable():
# destroy the default mysql connection
# after this line, when you use ORM methods
# django will reconnect to the default mysql
del connections._connections.default