Email attachments missing while forwarding an email in Salesforce Classic

This is currently Working as Designed. The feature "Save Email-to-Case attachments as Salesforce Files" saves the attachments as Files. In Classic UI, the files are not automatically attached to the forwarding of Emails and this is more of a Lightning Experience oriented feature, which is only supported in Lightning.

For forwarding emails with attachments via Classic UI, the user has to manually download the file from an existing email and attach to forward email.

See Also: 
Email-to-Case attachments don't get attached to the created case record.   

Configure Email-to-Case