It is not that easy to find information on Tunisian Berber, so I was quite happy to come across this PhD thesis free online: Berber ethnicity and language shift in Tunisia, by Hamza Belgacem. The author, himself from Douiret, estimates that only about 60,000 Tunisians still speak Berber, and the number is dropping as their children grow up speaking Arabic. He calls the surviving varieties Douiri, Cheninnaoui, Djerbi and Matmati, and argues that they together form a single Tunisian Berber "dialect" on a par with Kabyle or Tashelhiyt. (However, he offers no opinion on whether the extinct variety of Sened belongs with the rest, and forms this opinion on the basis of comparison to Kabyle and Moroccan varieties, but not Tumzabt or Chaoui or other geographically closer varieties.) This Berber community of southern Tunisia represent the remnants of a mostly Arabised tribal confederation, the Ouerghemma, which controlled much of southern Tunisia and parts of what became northwestern Libya until the French conquest.
He paints an interesting picture of a small minority language under the impact of modernity. Traditionally, the language was preserved by a number of factors tying the community together and excluding outsiders. The women of each community would marry only within it - not just among the Ibadis, but within the Maliki villages as well (as formerly in Siwa.) Some testimonies suggest that land was not sold to outsiders (a claim I also heard about Berber-speaking villages around Bechar.) Such ties are being loosened by modernity, as people emigrate and marry out and as the national state has taken on a more active role in the community with compulsory education and mass media. On the other hand, modernity, in the form of international media, also exposes the young to pan-Berber, or at least pro-Berber, ideologies, counteracting the low value placed on it in the national context.
Berber, and more specifically village, identity seems to have been maintained, with emigrants to Tunis maintaining close ties with other emigrants from the same village. But in terms of language, the balance seems to have tipped against Berber throughout Tunisia: "Some children of five years old could not utter a coherent sentence in TuB... Hardly any Tunisian Berbers under 30 speak TuB fluently but they may be able to utter a few words or understand what is said in Berber... hardly anyone under 10 years of age uses or knows TuB except for a few words or expressions", although there reportedly remain "certain clans, where the whole population still speak TuB, including all the children." There are a couple of pithy quotes from interviewees expressing why this happened: "Our language is excellent but it does not put bread on the table", "Our children are reluctant to speak our language outside the home because the other children of Arabophones laugh at them." The author suggests that Berber may survive in Tunisia if attitudes towards Berber continue to grow more positive, but that strikes me as a bit optimistic given his observations - which adds to the urgency of producing a decent description of the language.