Your quest timer will be reset to its original default time – since you no longer have the Double Quest Time Premium Perk. If over half the doubled time in your quest has passed when the timer is reverted back to its original time, the quest will be considered failed.
For example: If you have the Double Quest Time perk active and Jhudora gives you a quest you must complete in 33 minutes, if your subscription ends before you finish the quest, then the time will drop down to 16 minutes. If you didn’t complete the quest within the first half of your time – ie. the first 16 minutes – you will fail the quest when the timer goes down!