When you make a clone of a Soapbox Mailer campaign, it follows the standard Salesforce rules of Campaign cloning. This includes the fields that are copied from the Campaign record, as well as the related objects. Out of the box, neither Salesforce nor Soapbox Mailer will clone related objects' records, such as the Email Links.
So, when you clone a Soapbox Mailer campaign, the Email Links you've created for the original Campaign will not be copied.
This is actually a good thing. Why? When you create an Email Link, Soapbox Mailer tracks clicks on those links for that specific Campaign. This allows you to track the effectiveness of the same destination URL (say, your contact us page), across campaigns. If you used the same trackable link for all your campaigns, you wouldn't be able to know which one was related to which campaign.
We are looking at ways to automate the cloning of Email Links, and will provide updates here as we build this out further.