It should be noted that Stalinist USSR didn't crumble until Stalin died, they kept some of the airs for a time but it wasn't Stalinist anymore.
Now, on to your question. Why has North Korea outlasted any of its peers? There are a few reasons.
Concentrated power: the North Korean regime has a very concentrated power structure. There is no power outside of the top leadership. Kim Il-Sung started this arrangement because he admired Stalin and how he operated and his son and grandson added to the the structure as needed. The best example of this is the Seon'gun policy of Kim Jong-Il, he consolidated his power by leaning hard on the military for support and by multiplying the perks that top generals had. The Kims often give outright bribes to top generals or officials under the guise of gifts. They toss luxury goods at them to keep them loyal. If you are a high official or simply close to the Kims, you wield an impressive amount of influence. You might have a car, you might have access to foreign money which means you have access to foreign goods and blackmarket items and above all else, nobody beneath you can hurt you unless they also wield some kind of influence or if you make too many waves. But why would you be loyal if you aren't outright being bribed?
State "religion": North Koreans venerate the Kim family and the quasi-religious quasi-socialist system invented by Kim il-Sung called Juche. North Korea is officially an atheist state and society but in fact, it simply replaced what we associate as religion with a leadership cult. Over the years, the regime changed the education system, everyday life and even holidays to concentrate on them. The regime has fed generations of North Koreans myths about the leadership and the people have no means to share their skepticism because most North Koreans believe the myths and they might turn denounce you for being hostile to the state. They must participate in celebrations of the Kims birthdays, they must familiarize themselves with the words and teachings of Kim Il-Sung and they will, as early childhood, be held to certain standards of fanaticism about the first family of North Korea. North Koreans today genuinely believe that their country is better off than the rest of the world. The regime has an explanation for anything that might clash with its narrative. which brings us to the third point.
Propaganda: I chose to separate the personality cult from propaganda for a simple reason, don't get me wrong its all propaganda, but I wanted to concentrate here on the propaganda that the regime feeds its people about the greater world. North Koreans have been told that North Korea has the best leaders and the best situation and that any hardship North Korea faces is because of external factors. In addition to that, they push a vision of the world that is completely separate from the real world. Heres a video it'll give you an idea of what North Korean propaganda looks like. As a North Korean, you'll be bombarded by that type of thing everywhere you go. Your work, the street even your home. You've been taught to believe the state and the state is everywhere you look. Furthermore, the regime has all kinds of ways to put the Kims in the daily lives of regular people. From the pins of Kim Il-Sung that everyone must wear to the framed pictures of the Kims on every single building and in every single home and their mandated ritualized upkeep. It all serves to make the entire country focus on the leadership and the state. They provide you with everything you need from cradle to grave, unless of course, the evil americans are stirring up trouble and making it hard for the state to care for you... So, what happens if you start having doubts...
Repression: North Korean secret police are everywhere and the state has specific policies to deal with defectors or people that aren't unquestionably loyal to the Kim family. The best example is the three generations policy. Kim Il-Sung in the 70s, invented a new policy to deal with internal enemies. He introduced a policy whereby three generations of a family would bear the brunt of punishment for disloyalty, so, if your grandfather commits a crime, you will face the full force of the punishment meant for him. Simply questioning the regime is grounds for internment in political reform camps or concentration camps, depending on what exactly you did to question to state. Something as simple as not having cleaned the frame of the pictures of the Kim's that are in your house can get you sent to prison and the police will check on things as simple as those at midnight if they feel like it. They'll knock and come in. If you fail the inspection for any number of reasons, you, your kids and your grandkids are going to get punished. There's also something that is done at the job and neighbourhood levels called "Self-criticism" sessions, you appear in front of members of the party every day and you have to denounce the crimes of thought or of action that you committed since your last session... If you cause trouble, the police will use these sessions to convince you or any number of crimes. You will also be punished if you fail to report any kind of political crime.
There are a bunch of other measures taken by the regime that I wasn't entirely sure where to put. North Korea enforces a system of status called Seongbun, which assesses your family background and gives you your ascribed status in North Korean society. This status will dictate what you can and cannot do for the rest of your life, from the places where you can live, to the jobs you can have to the schools you can attend. It also maintains a system of food distribution which makes everyone dependent on the state even just to live day to day. The army also does everything from basic civilian plumbing to road maintenance, its everywhere and everyone must do their bit in the army.
This gives us a pretty good idea of why, in summary, the North Korean regime has outlasted any other: control. No one else in modern history has had this kind of control over its population. North Koreans cannot question the authorities, have no rights against anyone in a position of authority and they believe that they should be grateful for being so well off. It makes for a potent mix.
Sources:
Under the Loving Care of the Fatherly Leader: North Korea and the Kim Dynasty by Bradley K. Martin.
The Impossible State: North Korea, Past And Future by Victor Cha.
Nothing to Envy: Ordinary Lives in North Korea by Barbara Demick.
Edit: Thanks for the nomination to the Askhistorian Twitter account, thats awesome.