You cannot connect two Office 365 accounts in one Outlook profile at the same time

[Symptoms]

Some customers find that if they try to configure two or
more Office 365 accounts in one Outlook profile, these accounts cannot all connect
to the Exchange Online Server at the same time, even though you have configured them correctly. For example, you have name1@domain.com (default account) and name2@domain.com configured, when name1@domain.com is connected to the server,
you cannot get name2@domain.com
connected.

This issue may occur intermittently.

[Resolution]

To resolve this issue, use the Add-RecipientPermission cmdlet to add SendAs permission to the
default account. To do so, use the following steps:

  1. Connect Windows PowerShell to the Office 365
    Online Service

 

For detailed steps, visit Use
Windows PowerShell in Exchange Online
.

 

      2.  Run the cmdlet that resembles the following.
Please be noted that name1@domain.com is
the default account in Outlook.

 

$target_giving = 'name1@domain.com'

$user_getting = 'name2@domain.com'

Add-MailboxPermission –Identity
$target_giving -User $user_getting -AccessRights FullAccess -InheritanceType
All

Add-RecipientPermission $target_giving -Trustee $user_getting -AccessRights
SendAs

Note:  More details about Add-RecipientPermission
cmdlet
http://technet.microsoft.com/en-us/library/ff935839.aspx

 

IF this method does not resolve this issue, welcome to leave a comment here, or follow up on the original post http://community.office365.com/en-us/f/160/t/3505.aspx .