Some studies suggest that the benefits may persist (at least) for months.
That being said, it would be unrealistic for anyone to expect a rise in intelligence from a short cognitive training program to be permanent. After all, the effects of even the most powerful fitness program will eventually wear off if one stops working out entirely. By implication, you’ll likely need to keep completing n-back sessions on a regular basis in order to maintain the hard-earned cognitive gains from dual n-back in the long term.