Iberia seems to be a linguistic hodgepodge of Celts, other Indo Europeans, and pre-Indo Europeans. The topography of Iberia like the mountains in the north also tend to help increase linguistic diversity and helped preserve the sole pre-Roman survivor, Basque.
The Roman conquest of the region pretty much destroyed the linguistic diversity, and the upheavels of the Germanic invasions and later the Arab invasion finished it off. Despite this, it seems like a couple like Ceretanian (Basque-related?) and Cantabrian were alive to some degree or another as late as the eve of the Arab invasion. There's also Britonian, which has a similar origin as Breton.
So what are the odds any of these languages can hold out into modern times? I think the biggest thing is to make sure the Arab invasion fails (or never happens), and then establish a more organised state. Interestingly, the Ceretanian language was spoken on the same territory as Andorra, so a Ceretanian-speaking Andorra would be an extreme amusement on the tier of the Punic-speaking Malta I had a proposed in a thread a while back. Cantabria might also make a decent Basque analogue, although more of a rival more than anything going by the borders.
And aside from Ceretanian and Cantabrian, are there any others that have a shot?