Error: Unable to Receive Mail
The mail server denied access to the account "______" because an administrator or other mail client was using it when Mail tried to log in. Try again later.
The server returned an error: account is locked by another session or for maintenance, try again.

This error occurs typically when all available connections permitted to the user are in use. It is quite rare as most servers allow more than one simultaneous connection at a time. I last encountered this error when assisting a user with an ISP that only allowed one connection per user at a time. The user's iPhone had Push turned on so it was keeping a constant connection open preventing any other mail client from connecting. If you are stuck with a provider that only allows one connection at a time, try turning off Push notifications on the iPhone / smartphone or look for another provider like Gmail.