There were certainly descendants of Carthaginians living in North Africa after the destruction of the city. A preserved letter of St. Augustine gives evidence for the survival of Punic language, literature, and possibly a wider 'culture' up through the fifth century AD (http://www.newadvent.org/fathers/1102017.htm). As well, Punic was used in inscriptions throughout the area in ancient times after the destruction of Carthage. Overall it appears that religion, language, and some socio-political institutions survived.

Whether or not there were any groups as you have asked, I know of no evidence. It seems unlikely to me that there would have been any groups like neo-Nazis. The reception of Carthage after the 140s seems to have been quite negative. The ghost of Hannibal, after all, never really left Italy. There were also far more enemies of Rome, from both within and without, which could be used as real threats by people who wanted to undermine social and political order. Perhaps if Rome had not experienced such a tumultuous period in the first century BC there would have been something like you asked about, but that is purely speculation.

As further reading, most of the general treatments of Carthage do not have much for an 'after-life' section looking at Carthaginians, primarily because there isn't a whole lot of evidence. You may want to have a look at S. Lancel, Carthage: A History (Oxford, 1995), 428-438, and D. Hoyos, The Carthaginians (London, 2010), 220-223. Lancel is especially helpful and points to all of the evidence for the continuation of Punic culture in North Africa.