If an email address is the only email address entry on the constituent record, it can not be end-dated. The end-date date selector field being greyed out will only occur when the email address being edited is the only record.

If you need to stop the email address from receiving emails, then you can check the the option for "Do not send email to this address."

This topic is mentioned in our Blackbaud Idea Portal and can be viewed and voted on here.