I am writing this post for all those users who were using Windows Live Domains for their Business Emails and are currently facing problems due to their shut down (upgrade to Office 365).
Your business emails are configured on Microsoft Outlook formerly known as Hotmail.
The emails were made on Window Live Domains portal where one could use their own domain and create emails to make email accounts for your domain.

Last year, Microsoft closed the Windows Live Domains portal and migrated all the accounts to Office 365.
Now, all those users who have been using Windows Live Domain and created their business emails using it, they can continue using the emails without any problem. But now, they cannot sign in to the Admin Console, therefore, they cannot create any additional email accounts or even delete the already created ones.
Instead, they shall ask you to upgrade your account to Office 365.
Pricing: here

What is the solution now?
Solution No.1
You can stop using Outlook Emails and shift to some other third party business email providers like Google Apps for Business (recommended if you are willing to spend a little)
Google Apps for Business Pricing: here

Solution No.2
You can ask your website hosting provider to host the emails on the web server itself.
Cost: none (mostly all the website hosting providers give free business emails to configure)

Please note that you’ll lose all your data related to the emails when we’ll be shifting your emails to your web server.
To keep a backup, you can configure the old emails in Outlook Email Client and let it download.
Once, you can see all your emails downloaded, you can begin with the migration process.

In case, you are not able to back up your local computer, you will still be able to access your old emails on outlook.com as you did earlier but the only difference would be that the incoming and outgoing emails would not work.