Why can't I get a pending task in the Enablement tab to go away?

Pending tasks that are not removed might require action from your customer. 

Tasks appear under Pending Buyer Tasks if your customer needs to take action. Tasks that require your action appear under My Pending Tasks.

If the pending task is for your customer, contact them and request that they complete the task.

For details regarding the pending task "You have sent your customer at least one electronic invoice through Ariba Network" please see this article.

SAP Business Network