You have been identified as an Alumnus and as a result you now have an Alumni email account. This email account is guaranteed for life and is separate from your current Office 365 account, which will be deleted when your JHED account is closed. Typically students lose their JHED accounts 3 years after graduation but each school has its own policy and you could lose access as soon as 45 days after graduation.
Currently your email account is linked to your JHED account so you need an active JHED account to access your email. Your new Alumni email account, however, does not require JHED so even after you lose your JHED account you can still access your email with the new system. Rather than going through the portal, your new email account can be accessed from outlook.com/alumni.jh.edu using your new Alumni connect credentials.
In order to guarantee access to your Alumni email account and retain all your old emails you will need to migrate your email before your JHED account is closed. If you fail to do this your old email account will be deleted and you will lose access to all your old emails. To migrate your account please follow the instructions here: http://alumni.jhu.edu/alumniemailmigration.