The phrase "a problem that persists" is correct and usable in written English.
You can use it when discussing an issue that continues to exist or remain unresolved over time.
Example: "Despite numerous attempts to address the issue, it remains a problem that persists in our community."
Alternatives: "an ongoing issue" or "a continuing problem".
Experts like Bradley Myles, CEO of the anti-trafficking organization Polaris Project, have noted "there isn't much evidence linking the Super Bowl to a major rise in trafficking," while others point out that sex trafficking is a problem that persists not only during the Super Bowl, but year-round in communities of all sizes.
But the first section reveals a problem that persists throughout "4 x 4".
Freya Gill-Stevens, the promotions manager of the Leadmill venue in Sheffield, said it was a "problem that persists".
The haphazard cutting wrecks the moment with self-consciousness, a problem that persists through the long fantasy sequence in the middle of the movie.
Some worry that the lack of official birth registration — a problem that persists today, particularly in rural parts of the country — could have serious implications.
Ariel Weil, mayor of the 4th district of Paris, has called it "une invention de génie" (an invention of genius) that could solve a problem that persists in cities such as Paris, at least until it rains.
She says that's when she became a "hard-core bed-wetter," a problem that persisted into high school.
Late last year, the company told its suppliers that its accounts payable system was broken, a problem that persisted for about six weeks.
The shoreline erosion is a major problem that persist world wide and seawall still remain as one of the most widely adopted coastal protection structure.
The celebration of his poor performance was not ideal, and being famous for not being very good at something is a problem that still persists in this country today, but who among us would have turned down the chance of fame that came after all that Edwards had put himself through?
And so this is a problem that has persisted.
