An email address must be present within the Contact Card for the respective correspondence to/from that address to be linked to the record. If an address is removed from the record, all correspondence from the address will unlink from that record and will no longer be visible within Email History for that record.
In order to maintain email history for an email address no longer in use, select the Actions menu for that address from the record's Contact Card and choose "Archive Address". This will hide the address from display, but keep the email history intact.
For detail information on how the archiving works, please click here.