First, a little background information. AC Master is designed to work when you don't have an internet connection, so you can take it out to a practice field or trial site far from technology and still use it's most important features.
AC Master also has you log in so multiple people could use the same app on the same phone or tablet and keep their data separate. In order for you to log in, you do need a network connection so AC Master can verify you are who you say you are. Once you are logged in you can go offline and online and the app still works normally.
When you log out it "forgets" your sensitive login credentials (and keeps your data stored).
Now back to the question. if you accidentally logged out when offline you wouldn't be able to log in again until you had an internet connection. That would keep you from using AC Master. So if the Logout button is disabled it is likely you are offline. Once you have a connection the Logout button will be active and you can log out.
If you often use AC Master "off the grid" stay logged in and it will always be ready to use!