I can log in to my account only once and then I get kicked off with "Mail is currently unavailable" coming up, and then I am unable to log in again.

Hi Tree,

Are you using the built-in metro store apps "Mail" or the office software? What is the type of the account?

To troubleshoot whether this issue is caused by the specific account, we could try to login from the website online to have a check.
We also could try to login with another account to have a check.
If you are using the built-in metro apps, we could refer to the following link to have a troubleshoot.
Troubleshoot problems with an app
http://windows.microsoft.com/en-HK/windows-8/what-troubleshoot-problems-app
In addition, we could run "wsreset.exe" to clear the cache to have a check.
If the issue proved to be related to the specific account, we could wait for a mement to have a check and it is recommended to ask for help from the account support.

Best regards