Historical note, per Wikipedia:
The island was attacked in 88 BC by the troops of Mithridates VI of Pontus, a staunch enemy of Rome, who killed some 20,000 of the resident Romans. Another devastating attack was by pirates in 69 BC. Before the end of the 1st century BC, trade routes had changed; Delos was replaced by Puteoli as the chief focus of Italian trade with the East, and as a cult-centre too it entered a sharp decline.
Due to the above history, Delos unlike other Greek islands did not have an indigenous, self-supporting community of its own. As a result, in later times it became uninhabited.
I can well imagine though clearly not as well as pianist Emily Bear, who’s been there:
As of 2001, Delos had a population of 14. By coincidence, Emily will be 14 this month.