Dacia was one of the first provinces the romans abandoned. Yet the current inhabitants still call themselves romans (Romanians). How did the culture or maybe just the language survive that long even though the region was abandoned and the neighbours weren‘t particularly friendly?

I will add a little bit to /u/Spoonfeedme's comment. Mine is mostly about the importance of the "Latin roots" of Romanians as seen during the XIX century and why this is a hot debate topic among the general public in Romania, but also Hungary.

In the very good comment by the other redditor, you will find out about the conquest of Dacia and the two hypothesis that exist today. I will add a little bit to the aftermath of Aurelian's retreat.

As you may know, Dacia was a Roman province for only a little bit (by historical standards) and answering how someone could remain latinized after not even 3 centuries of Roman rule is tricky. Especially since records are scarce. This is actually the main problem. The lack of record. We literally do not have writings from this region. Only from Byzantium, the Russians a little, the Hungarians after they came etc. The first text in Romanian is in 1521 (Neacșu's letter) , more than a millennia after Aurelian's retreat.

Comparison's with Britain is made. My professor made it also (I studied history in Romania). We can trace the evolution of English through the centuries of the Early Middle Ages. No such thing for Romanian.

In defense of the "continuity hypothesis", unlike Britain where small kingdoms or political entities were established after all, in Romania we did not. Both former provinces experienced migrations, but they are different. Many tribes came and go in the east (Gepids, Cumans, Huns, Avars etc.) and did not had a lasting political entity. Unlike Britain where we have a relative good view of the political developments in the era. Also, the Empire just went south, and so, the story goes, kept economic ties through trade for centuries and thus, romanization continued in some form.

Romanian historiography during communism put some emphasis on the Dridu culture. They are populations south of the Carpathians that left traces (pottery ant the likes). They are very rural and the quality of they pottery is nonexistent. Even some Neolithic tribes have better pottery. While many findings form the era are known during communism as Dridu, some are not. The historians back then wanted to show a large presence of them as they were considered a remnant of the Romanized people and thus highlighting continuity. Nonetheless, they existed.

The weak spots of the continuity theory it is based on many suppositions that can not be verified with chronicles of the time, large archaeological findings (this is also a problem, after 1989 the funds for excavations are very low). We can not prove that those who supposedly took shelter in the mountains kept their language. We do not know how their language looked like.

Now for the migration hypothesis. It may explain some stuff like the fact that Romanian has relative few differences in language, or the many toponyms that do not have Latin background. On the other hand, a large migration leave traces. We know when the Slavs came in the region, the same for Hungarians or other people. We do not have evidence for a south-north migration made by Romanized people. The Byzantines must have made some mentions. They usually note important events, especially since the Balkans are their POI until the very end and Vlachs are mentioned a couple of times. This being said, it is not impossible that a small scale (but for long periods) migrations could have existed.

Bottom line, because of the lack of historical records, we can not reach a conclusion. The pure "continuity hypothesis" with shepherds who await their time for things to settle and then becoming the largest population group by 1200 is far fetched. The pure "migration hypothesis" of a terra incognita where an entire population group arrives without anyone mentioning it, is also far fetched.