Have you checked "Permit end use to perform" check in advanced Wait options? Also could you share design time configuration screenshots for Wait shape. What is the workbasket provided? Does user have access to that workbasket?
Can you pls check the workbasket configuration? If you have mentioned the role in workbasket rule form then users having that role will have access to that workbasket. Other users won't have access. At the same time Agent will fail to move the assignment due to lack of access.
Pls also verify the Broken queue items from designer studio. This will tell you the reason of SLA failing to move the case.