Load balancing read only SQL 2008R2 servers

You probably want to modify the value of the Action on Service Down setting for the Pool. The default is none, if you change it to Reselect LTM will select another Pool Member and ‘rebind’ the client-side connection to a new Pool member.

If authentication is involved however I'd imagine things would still break. If you use persistence for that reason or some other reason, things will break, application wise.