How long the store stays open will depend on when the lease ends or what the buyout options are to end the lease early.
The only time they would shutter a store outside of lease termination is if the store is losing so much money that it is less expensive to shut it down and eat the rent until the lease expires or the space gets re-rented than continue to pay the operating costs to run the store.
As others have said, closing sales usually run 8-12 weeks to clear out all the non-returnable inventory but they will cut off replenishment of those items 4-6 weeks before that. If your store suddenly stops getting toys restocked after the holiday shopping period, you know your in trouble.