With Blizzard officially revealing the start date for Mists of Pandaria Timerunning, they've also given us a good idea of when it will end, as The War Within Alpha client lists the event running from May 16th to August 19th!
While this is not yet officially confirmed and nothing on the Alpha is definitively final, the fact that the start dates match makes it likely that the end dates will as well. This gives players three months to enjoy the remixed content and chase its huge collection of rewards.
WoW Remix: Mists of Pandaria Timerunning Overview
These dates also tell us that Patch 10.2.7 is set to release one week prior, on or around May 7th, although the other retail content coming with the patch has yet to be revealed.