I ran into the same problem and I found out that the Customer Portal is not able to show any attachments added to the ticket through the JIRA interface.
The way I solved this problem was by uploading the attachments through the Customer Portal, instead of the JIRA User Interface.
Now, if you have attachments already added to the JIRA ticket and you want to expose them to the client, you can add a public comment ("Respond to customer"), and add the following markup tag to display the attachment.
[^atachment_name]
Don't forget the "^" symbol!
This should display the attachment as part of the comment and make it available to your customers.
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