I would imagine when you connect from your local it is registering a new server in the web farm, and then probably over your limit of number of servers.
You can set your web farm to manual, then in the web config(or azure app settings) of the MVC and Admin sites, add this setting:
<add key="CMSWebFarmServerName" value="Admin" />
Then you just need to create the servers under that name in the web farm app. If your local instances have different names in the web config, they shouldn't register.