Whether or not the landlord can require the commercial tenant to remain open during a certain period of time would be best addressed within the presumed written lease agreement that you have in that its terms and obligations control the obligations owed to you by the landlord and vice versa in the absence of conflicting state law.If the written lease states no specific hours for you to remain open, then you are not contractually obligated to do so. If it does, then you are. I suggest that you first meet with your landlord about the request on store hours to try and resolve the situation. If you are unable to resolve the store hour situation, I recommend that you meet with an attorney that practices law in the area of commercial leases to further assist.