While I can't speak to the Illyrians specifically, I can say that the Romans and Greeks were either not terribly good about recording information about their "barbarian" neighbors or said information simply failed to survive the two thousand years between us and them.

When Romans or Greeks wrote about history, they tended to write about their own affairs. Tacitus, despite writing Germania, wrote more about Roman history than of foreign tribes. Authors like Livy and Suetonius only wrote about Roman matters (History of Rome and the Lives of the Twelve Caesars, respectively). For every Germania, there were five Histories.

The other important factor to consider is that works have rarely survived intact. If we consider Cato, for instance, we can read about his history of early settlements in Italia... but this work is incomplete. His work on farming, however, reached us intact. And while it's rather unlikely that Cato wrote about the Illyrians in any detail, we see this pattern of incomplete works on the subject of history run through much of Roman history. Even though The Annals contains, at best guess, 16 books (because we have Book #16), Books #7-10 failed to survive. And so, because of the vagaries of time, we're missing Tacitus' assessment of Caligula's reign, among other things. And there are works of authors we have lost wholesale: despite Tacitus referencing him, we lack (to my knowledge) any surviving work by Rusticus, whose works may simply have been buried in the Roman Senate's archives and then lost. The works of other historians, such as Titus Labienus, were deliberately destroyed -- sometimes by the Roman state itself, as in this specific case.

All of this serves to explain why, for the most part, Greco-Roman writers failed to hand down histories of many of the peoples that bordered them. The Byzantines would prove a fair bit better at this than their predecessors (much of what we know about the Huns, who show in their records as 'Royal Scythians,' comes from Byzantine sources), but that may simply be a matter of proximity on the historical timescale: those works only had to travel half the distance that works by authors like Sallust had to travel.

It's also probably worth noting that a fair number of historians in that period wrote about other subjects. Plutarch (a Roman-era Greek historian), for instance, is probably most well-known among historians for his series of biographies of historical figures. But he also wrote about Greek and Roman social norms, which isn't something we have terribly many sources for. And he wrote some damning criticisms of Herodotus that are frequently amusing.