The reason of a delay is explained by a lack of the source material. Nanbaka is based on the manga of the same name, which contains only six volumes. Two full seasons of twelve episodes (or rather two cours) + an OVA have covered the entire manga by Sho Futamata. In fact, you are waiting for Nanbaka Season 2 not 3 since there has been just one season split into two cours. However, since most of the broadcasters decided to treat these two cours as two separate seasons, we will follow such a rule.
In general, Nanbaka Season 1 was a success. According to MyAnimeList, the first installment of the anime holds a score of 7.42/10 based on about 60,000 votes. The 2nd season has received a score of 7.62/10 based on ~ 28,000 votes.
Yet still, despite quite a favorable reception from the target audience, we tend to think that Nanbaka Season 2 won't happen. Looks like, the story source is exhausted. We won't see Nanbaka Season 2 until at least six more chapters of the manga are issued. However, given the fact that the sixth volume has been issued in September 2017, the franchise looks suspended.
Of course, we don't rule out that Nanbaka might go out of a long-term hiatus. Yet such positive scenario looks quite unlikely as well. As a rule, we may make a positive forecast when we see that a franchise is ongoing. Nonetheless, in the case with Nanbaka, we have not seen any changes since 2017.
Summing up, all indications are that Nanbaka won't return for Season 2. Such information might look a sad news, but it's much better to know the truth. Of course, we are looking forward to the official announcement of renewal. But there have been no updates of the Nanbaka franchise within two years.
So guys, don't trust any weak sources. There have been no news and even leaks about any possible renewal. If you don't believe us, you might visit the official website of the anime, which is, by the way, is unavailable as well. We were managed to find a copy of the website in a web archive. However, the last news is dated 2017. It's better for you thereby to come to terms with the fact that the Nanbaka franchise is dead.
The story follows four guys who are currently serving a sentence in Nanbaka, a prison whence no one managed to escape since the prison walls are high, and the facility is protected by the best security system. Similar to other Japanese prisons, all the prisoners in Nanbaka are split into groups, where each prisoner is numbered.
Hajime is a supervisor in the Building # 13. His life could be boring. Yet thanks to the four, he must be always on the alert. Jyugo, whose number is 1315 is the one who usually elaborating the escape plan. Uno, # 1311, is of British descent, who is a con artist, as well as a misogynist. Rock and Nico are two Americans, whose numbers are 1369 and 1325, respectively. One of them is a bully, while the other one is an otaku. The four know how to have fun, even being imprisoned.