"persistent curiosity" is correct and usable in written English.
You can use this expression when you want to describe a continuous or enduring interest in a particular topic or subject. For example, "He maintains a persistent curiosity about the history of the town in which he grew up."
Asking questions was 'being tiresome,' while persistent curiosity got one nowhere, at least nowhere of interest".
Mr. Barnet's good work, it turns out, comes throughout a career of persistent curiosity and eccentric coherence.
He has an elaborate surprise planned, and when it is ruined (by his clumsy eagerness and Violet's persistent curiosity), he goes through with it anyway.
If anything links these disparate subjects it is, one guesses from various prefaces and acknowledgments, Bobrick's persistent curiosity about his own family -- his forebears fought on both sides of the American Revolution, for example, and his mother crossed Siberia alone in 1929.
It remains unclear whether Hines pitched the article or was commissioned to write it, but the sex lives of athletes at the Olympic Village is a source of persistent curiosity at every Games, and Rio's "record-breaking haul" of condoms was widely reported on last month.
In fact, those who invent, who thrive intellectually and often, in work and play, have a persistent curiosity; they are inspired and they are motivated.
There are already bad books on the subject; this one is good, the product of persistent, gentle curiosity and persistently open eyes.
He was speaking after Australia's first practice session under their new coach, Darren Lehmann, and there was much persistent, but polite curiosity about how it went.
Casanova's persistent, fox-like curiosity is matched by Dracula's stolid hedgehog charisma, but Serra disperses their energies and their conflicts throughout the film, by way of an astonishing repertory of eighteenth-century sounds and sights.
