Jan 8, 2014
Welcome to the PlayStation Community.
Yes, so long as you re-subscribe you'll be able to continue playing the 'free' games, the expiry date you're seeing will update when your current suscription expires in 6 days.
Customer Service - 1-800-345-SONY (7669)
Account & billing Support -1-877-971-SONY (7669)
Available Mon to Fri 8am - 8pm PST