Yes, Dubai Duty free is open 24 hours. The 'main' duty free area is only accessible when departing from Dubai, although there is a smaller section available on arrival next to the 'baggage claim' area. Don't forget, 'Duty free' items are also available on all Emirates flights. This depends on the nationality stated in your passport and the amount of time that you are in transit.
Most nationalities require visas to enter into Dubai, and regulations frequently change.
If you do intend to leave the airport while in transit, please check your visa requirements with the local embassy before you start your journey. All Rights Reserved.