The phrase "a persistent example" is correct and usable in written English.
It can be used to describe an example that consistently appears or is repeatedly referenced in a particular context.
Example: "The study provided a persistent example of how climate change affects local ecosystems."
Alternatives: "a recurring example" or "a constant example".
The most persistent example of such a legend is that of the Kingsale hat.
Sammy Glick is merely the most vivid and persistent example of what has become over the last 75 years one of the stock characters in American popular culture -- the Hollywood wheeler-dealer.
Still, the recent study by Ms. Chen and Ms. Chan found persistent examples of dangerous exposure to benzene and other toxic chemicals in larger, export-oriented factories, mainly Taiwanese-run, in the coastal province of Fujian.
Because of the portability of works such as paintings, as well as their concentration in museums or private collections, there have been persistent examples of major thefts of art.
Now, 130 years later, the school still works toward furthering the understanding of psychic abilities, using new scientific techniques to work out whether stuff like astral projection and dowsing have any kind of rational explanation, are truly supernatural, or are just persistent examples of New Age bullshit.
A persistent bleeding, for example after surgery, is indicative for a primary hemostasis problem, whereas a delayed bleeding is more suggestive of a secondary bleeding disorder.
If the pain recrudesced in less than two hours or there was a persistent pain stimulus (for example, surgical scar, drains) a continuous infusion of fentanyl would be initiated and titrated by the attending nurse using numeric pain scale (which measures pain from 0 = no pain, to 10 = the worst pain ever experienced) aiming a value ≤ 4.
There is a persistent supposition – see, for example, (Gilson 1937) – that Ockham, and many of his fourteenth-century followers, had a basically Humean position on causality; this supposition has deep historical roots (Nadler 1996), but is inaccurate (Adams 1987, pp. 741ff).
For example, a persistent relationship between low SES and increased overweight and obesity prevalence has been reported in several studies focusing on Australian youth [ 20, 28, 29].
The PBDE case study was developed to provide an example of a persistent compound for which relatively few data are available for human exposure, biomonitoring, and health outcomes.
