Upon the pressing of the Send button, every Soapbox Mailer Campaign creates one Apex Job and within that job multiple batches (one batch for each email sent). If you ever need to take a look at a more detailed status of an executed email campaign, you can find more information within the Salesforce Apex Job monitor. Here's how to get there.
1) Login to Salesforce and go to Setup > Administration Setup > Monitoring > Apex Jobs
2) On the Apex Jobs page, look for any jobs that have the Apex Class value listed as "UpdateCampaignMembersEmailBlast", which will be the Soapbox Mailer campaigns you've sent