With Mists of Pandaria Remix now live in all regions, a notification on the character select screen indicates 95 days remaining in the event, confirming the previously speculated end date of August 19th.
Whether or not the Timeruning end date has any relation to The War Within Pre-Patch is still anyone's guess, though it would seem like a pretty natural transition for a mid to late summer release date, expecting The War Within pre-patch around the end of August.