In fact, we are faced with the same problem.
At first I contacted Azure support (paid for it), but they could not help me (from overseas Azure). However, the support engineer was so kind as to send me another link for Visual Studio support: http://www.visualstudio.com/en-us/support/cloud-services-assisted-support-vs . This connection did not actually work on the first day, but it did work the next day. Therefore, I admit that I was initially disappointed with the support.
However, through this link (the next day) I can send my problem. I got an answer after 8 hours with an answer that helped me solve the problem right away.
The answer is:
The user must install and then log in to this VS PRO using the same email address that was assigned the license in the VSO user concentrator. The user also needs to make a choice how to enter the \ license: OrgID or Microsoft account (MSA). The right choice will depend on the support of the Azure Active Directory VSO account. If so, the user should use the OrgID option. Otherwise use MSA.
However, be careful. If you click on the organizational account in “Licenses with a different Microsoft or Organization account”, you will be directed to a window in which the dominant part is a control for entering the Microsfot account. You can activate remakr so that your account does not exist. First you need to click "Log in to your Organization account" on the left side of the window.
Than everything worked smoothly.
The local license was updated with a monthly subscription (of course, an Internet connection). He said something was about to expire in 30 days, which was expected because of his monthly subscription. As long as you continue to pay your Azure bill, although you have an Internet connection to upgrade your license, you will continue to work with the IDE VS 2013.
That said: we apply this procedure 3 months ago, and then it did not work. At that time, we read Login to Visual Studio with an organization account, and not with a Microsoft account , which was virtually impossible (for now) with an organization account.
Therefore, I assume that some improvements have been made at the same time.