A quick Google search turns up a number of theories on the etymology of the name Tabelbala, none of which correspond to the one that old men here tell me, which appears to me to be much the most plausible. The oasis' name is Tsawerbets in Kwarandzie, Tabelbalt in local Tamazight, and Belbala in local Arabic; they derive it from a tree called awerbel in Kwarandjie and belbal in local Arabic, that used to be common but (presumably due to the lower water table) no longer grows here. [e=schwa] It turns out that belbal is fairly widespread in North African Arabic, and refers to a type of pine; it's also attested in Taznatit, as abelbal. The normal Berber diminutive gives tabelbalt, and the usual Kwarandjie shift of l>r and t>ts would give tsaberbelts; intervocalic b>w is irregular, but I have heard it in other contexts, and final clusters tend to be simplified, which would give tsawerbets. Berber diminutive morphology is not productive in Kwarandjie, so it's hard to imagine this being a folk etymology. If this is correct, the very name of the oasis, like its many acres of ruins and its hundreds of dried-up foggaras, is a mute testimony to a time not too long ago when it was much greener and wetter.
At the moment, Kwarandjie turns out to have roughly on the order of 3000 speakers, adding up the populations of the three villages as given to me by a local official (himself a speaker) and assuming the minority that doesn't speak it at all is made up for by all the emigrant speakers in Tindouf and Bechar. This represents about half the population of the oasis; the other half is in el-Kartsi (le Quartier), the newer town centre. Despite the endangerment discussed in the previous post, this is larger than it's been at any point since 1908, when Cancel counted barely 500 or so speakers. But even in Cancel's time most of the foggaras were dry, and a few centuries earlier refugees had fled the area for places like Mlouka and Ktaoua; in earlier periods the number of speakers may have been significantly larger, judging by the ruins of their houses, which seem to cover an area rather larger than the present settlements do. That former climate might help explain why the oasis not only kept a language that has remained practically nowhere else in the thousand kilometers between it and Timbuktu, but also kept much more Songhay vocabulary than the other northern Songhay languages - even words like hawi "cow", referring to items currently totally absent from the oasis, or tsyu "read" and genga "pray", referring to concepts strongly associated with Arabic. The historic decline in the oasis's population and prosperity has surely itself had its effect on the language, letting words associated with particular specialties (perhaps silverwork, for example) to vanish for lack of customers to sustain them, or ones for species to vanish with their referents (as the word asiyed, "ostrich", has nearly finished doing - I've only found one speaker who knew it, although Champault confirms it). But is there any way to prove the existence of such an effect, or measure it?