SLA stands for Service Level Agreements. The agent name to look for is ServiceLevelEvents. You can check for broken queue items by looking in SMA (Agent Management > System Queue Management screen) or in Designer Studio (Process & Rules > Tools > Work Admin > Broken Queue Items).
You would select the System-Queue-ServiceLevel class and click Execute View. You can check to see if there are any Broken-Process items for your work object. Another thing to consider is what happens in the flow after the Wait shape. In one of your screen shots, it looks like there is an End shape after the Wait. Should the work object be resolved at this point or does it go to another flow? If you are eventually routing to another assignment, you will want to make sure you are either routing to a specific workbasket or user. If you are using Current Operator, it will fail because the agent is the operator processing the Wait shape.
When that flow ends, where does the stack unwind to? Does the item get resolved? Does your user fire off the HappyEnd flow action or is that done by the SLA on the previous assignment? If it's not done by an interactive user, are you sure that perhaps the problem isn't upstream? If the user does take the action, what happens to the item? Does it get put onto a review harness (which what status)? Do you see this same problem if you stick an assignment between the wait and the flow end?
>>> As I understood the wait should not be in one workbasket? What do you mean Current Operator?
When your flow is running from your own login, and let's say you log in as "joeUser", the current operator is "joeUser".
But if the flow uses SLA's, which some wait shapes do, then when that SLA is running in the agent, the current operator will be "system".
If you ever do routing in your flow, it's important not to route to "current operator", particularly if that routing will be occurring in the SLA, since that routing will fail when it attempts to route to "system".
Usually, the solution to that problem is to make sure you are routing to something more explicit like a particular work basket, or a particular user.