Chenanith b'Libya - in the 11th century AD?

Anyone interested in North African languages who doesn't speak Dutch should immediately check out Bulbul's posting on Latino-Punic. The Phoenicians brought their language with them to North Africa when they founded Carthage and other cities. Carthage was destroyed, of course, but many other cities continued to speak Phoenician for longer; however, like Arabic in more recent times, it changed a lot under Berber influence, and this later dialect is usually called Punic. This language was spoken by St. Augustine, who quotes a number of Phoenician words, such as salus (< shalu:sh < shalo:sh < shala:sh < thala:th) "three", in his works. In eastern Libya, as it happens, Punic continued to be written even after the Phoenician alphabet was forgotten; this body of inscriptions, using the Latin alphabet to write Punic, is called (logically enough) Latino-Punic, and a comprehensive database of such inscriptions is available from Leiden. Recently, as Bulbul points out, a thesis was submitted at Leiden on Latino-Punic and its Linguistic Environment; I would love to read it.

The twist in this tale is that Phoenician may have survived into the 11th century AD! Al-Bakri (whom I've mentioned before) enigmatically says of the inhabitants of Sirt in Libya that:

لهم كلام يراطنون به ليس بعربي ولا عجمي ولا بربري ولا قبطي ولا يعرفه غيرهم
‍They have a speech in which they jabber which is neither Arabic nor Ajami (by which he probably means Latin but might mean Persian) nor Berber nor Coptic, which no one but them knows.

The location (in eastern Tripolitania) is about right for it to be Punic, and if it were Greek you would expect him to know, considering he cites (more or less correctly) the Greek etymology of طرابلس (Tripoli) in the next page. So was Punic still spoken in the 11th century? Your guess is as good as mine, but it looks plausible.