If they aren't willing to raise their limit of persistent connections for you, then there is nothing you can do unless you choose to change hosts.
"MySQL Server has gone away" is a server issue. See this:
https://www.vbulletin.com/docs/html/...mysql_goneaway and this:
https://www.vbulletin.com/forum/show...265#post310265 You will need to talk to your host about this in order to get it resolved.