Nazi Germany annexed all other territory ceded to other nations in the Treaty of Versailles, why did they not take back this region?
Sure enough there were high hopes of the german minority that North Schleswig would be returned to Germany once the Nazis had the power to enforce this. From 1932 on the Nazi program found great approval rates within this group, who never had lost faith after 1920 that one day they would be german citizens again. During 1933 many Nazi parties were founded in North Schleswig, that would ultimately be united in the NSDAP-N (National Socialist German Workers Party - North Schleswig) in 1935.
But when the calls for reappropriation of North Schleswig by Germany became louder and louder, in North Schleswig as well as in german Schleswig-Holstein, causing rising concerns in Denmark, the agitators were ordered by the Nazis to keep quiet. The role intended to the germans in North Schleswig by the Nazis was that of propagandists of the Great-Teutonic ideas in Denmark and as intermediaries between Germany and Denmark. When the demands were revived after the occupations of Austria etc by Germany in 1938/1939 this just earned the agitators sharp rebuke by the Nazis.
When Germany invaded Denmark 9. April 1940 it was officially to defend it against the imminent threat of invasion by the allies. Inofficially it was also to secure the supportlines to the strategically more important Norway and to gain imports, predominantly food, from Denmark.
Denmark surrendered after just a few hours. This was not just due to the realisation that further resistance was futile but also because King Christian and the government had been assured, that Denmark would stay idependent, officially even neutral. Part of this independence was, that police and military would stay under danish control (they did, until 1943), that the danish constitution would remain valid (in 1943 elctions were held, with the Nazi party just gaining about 2%) and that the territory of Denmark would stay intact - a real bummer for the germans of North Schleswig.
There were several causes these concessions were made so easily. First off danes were according to Nazi ideology just as aryan as the germans themselfes, so treating them as good as possible would surely make sense, especially since Denmark had, in contrast to Norway, offered just very weak resistance and the governmant did actually cooperate quite well with Germany, until it didn't in 1943.
Then a good treatment of Denmark would certainly make for good propaganda, especially towards neutral states.
Also there was the thought that Germany would have to deploy less troops in Denmark if the danes on the one hand had as little cause for discontent as possible and on the other hand were controlled by their own police and army.
When the Nazis especially from 1943 on had to realize that most notably the latter didn't stand the test of time they had other things to worry about than an annexation of North Schleswig.
Sorces:
https://edoc.hu-berlin.de/bitstream/handle/18452/8558/2.pdf?sequence=1
Mazower, Mark Hitler's Empire: Nazi Rule in Occupied Europe
Bonus: The occupation of Denmark and Norway shown by the Nazi News Reel:
https://www.youtube.com/watch?v=8gZQcPyL-zI