Call, Request and Task all seem to be missing a 'Complete' button of some kind when in the Call/Request/Task. In order to close anything, the analyst seems to be expected to set all the fields, click Save, have the tab close on them and then locate the Call/Task in the Outstandings list and right click it to Close it. In Core you just have to click the Complete/Close button at the bottom of the page.
The inclusion of this button allows you to manage your Calls and Tasks more efficiently.
You close a call or request by changing the status of the call or request to Completed (or whatever your organization considers completed. Look in your system admin settings.) For Call's a Resolution\Conclusion box will appear (if you didnt hide it) and you fill it in. Click save. For Request chose complete and save and the workflow moves to the next task.