The issue is not with MySQL, it is just how your load balancer is checking the health, by attempting to “connect” to MySQL, instead of using MySQL’s actual “ping” functionality.
To get around this, you could set max_connect_errors to a larger number, which would prevent MySQL from blocking the load balancer. However that would apply to all connections, so it could cause issues with other things if you get flooded with connections.
Another alternative would be to run mysqladmin flush-hosts via a cron task, which would clear out the error count before the IP got blocked. But again that could cause issues if you get flooded with connection attempts from another source.
Outside of that, you’d have to modify the way your load balancer is checking MySQL health.