Always logged on. No matter what.
As for the core issue itself, if you reinstall the Mobile Armory, go to Guild Chat with the character that is experiencing the issue, login, and then sign out of Guild Chat (not the app itself). Once you've confirmed that you're offline, log out of the app. Now you can uninstall.
If you signed into multiple devices (phones, tablets, portable music devices, etc.) with your account, you may need to perform these actions per device.
I very rarely encounter this myself but these steps have been proven to work in most cases, as this should hit all of the WoW status logic related to logging you out and placing you into an Offline state.
Please report any Code of Conduct violations, including:
Threats of violence. We take these seriously and will alert the proper authorities.
Posts containing personal information about other players. This includes physical addresses, e-mail addresses, phone numbers, and inappropriate photos and/or videos.
Harassing or discriminatory language. This will not be tolerated.