After the sack in 396 BCE, her territory was divided up among the Roman citizens. Camillus argued, however, that the place should not be occupied by Romans and become a second capital (Livy 5.29-30). And so it was, apparently, left abandoned but with structures largely intact. Six years later the Gauls came, and after the Battle of the Allia the Romans retreated not to Rome, but to Veii. When the Gallic nightmare was over, some of the Romans apparently got a little lazy and decided that it was easier just to stay in the abandoned structures at Veii rather than go back to Rome to rebuild. They ignored a senatus consultum ordering them to return but were eventually forced to do so (Livy 6.4).

The history of the site after that is uncertain. Caesar may have put veterans there, but we know that in 2 BCE Augustus founded a very small Roman settlement there called municipium Augustum Veiens, and several inscriptions discovered in the vicinity show (part of) this name. It was never an important place, but in the Julio-Claudian period we hear of members of the Tarquitia Priscus family there, who may have had tenuous connections all the way back to the Etruscans of the once-proud. At some point the site was abandoned or destroyed (in late antiquity), and gradually the location of the place was forgotten. In the early medieval period a castle was constructed on what was probably part of the original city, at a place now called Isola Farnese.

There is a very important Villanovan culture site in the general neighborhood. A recent "re-study" covers this and other interesting points (review here). I haven't seen it myself but am told it is really great, and has a good historical introduction by Smith.