Thanks for your response, David. I can confirm that load balancing is hopping between servers when in the admin tool. We have a session state server and a single database, but there must be other differences when switching servers. Investigating further, if we may need to check the load balancing configuration.
Does anyone know of any documentation that has guidance on load balancing configuration? I know there are a lot of devices, but any sort of general guidance would be better than nothing. All I can find is pretty generic hosting specs that mainly talk about the web servers and how to configure the web farm in Kentico.