Sandbox campaigns do not run automatically by design. This is for reasons surrounding Campaign Management, Resources, and Security.
To run a Sandbox Campaign:
1. Go to Support > Schedules
2. In the upper right-hand corner, choose the campaign type that you are currently testing. This will load the list of campaigns that fall under this category.
3. To the right of the campaigns, you will see a "Run Now" button. select this to run your campaign.