Are you using MVC? I mean the live site apps are MVC? If yes, then the CMSUseAutomaticScheduler has no impact here since the scheduler is executed on the Kentico admin app, not on the MVC apps. It should be enough just to have the automatic web farm configured (this is useful for auto-scaling). But, you can try also the manual web farm mode to see if it makes any difference. If not, then the issue is probably in the load balancer and/or the network between the Kentico app and the MVC apps.
By default there is a ping made every 20 seconds to the web farm servers. If there is no response on the ping, server goes to Transitioning state for 3 minutes. Within these 3 minutes, if the ping is still failing, server goes to Not responding state or if the ping starts answering, servers goes to Healthy state. So, maybe there is some connection issue too.
Sometimes it helps also to delete all web farm servers from the admin app (Web farms) and when using automatic mode, let the system to generate new instances.