The phrase "a persistent problem and" is correct and usable in written English.
It can be used when discussing an ongoing issue that continues to affect a situation or context, often leading into further explanation or related points.
Example: "The team has been facing a persistent problem and is actively seeking solutions to improve performance."
Alternatives: "an ongoing issue and" or "a continual challenge and".
Unemployment is a persistent problem, and many residents work abroad, especially on Ascension Island.
Army officials said that a persistent problem, and one that had delayed this assessment, was a lack of standard testing procedures across the armed forces.
Away from the office towers and rooftop cocktail lounges, long-term unemployment is a persistent problem, and young job seekers are losing hope, Mr. Jones said.
An ankle injury has been a persistent problem and has taken the edge away from his running, which is the third of the disciplines and the one where he normally has the biggest edge over opponents.
Medication errors are a persistent problem, and researchers are now investigating a new category of safety concerns: diagnostic errors that affect at least 12 million patients a year, with 4 million suffering serious harm.
Data leakage has been a persistent problem and companies have closed up some of the problems by restricting access to USB (universal serial bus) slots on the side of computers, encrypting data at rest meaning inside a notebook computer so if it gets stolen it takes a supercomputer to crack the code and using revolving passwords that are invalid after just a few seconds.
Enteric fever is a persistent problem in Kathmandu and in other urban locations in South and South-East Asia [7], [26].
"Illiteracy is a persistent problem in America, and it's steadily growing," said Mr. Billington in an interview.
Energy storage is a persistent problem in general and electrical energy storage in particular.
Malnutrition is a persistent problem in hospitals and intensive care units (ICUs) worldwide.
Discussions on education issues with parents and committees highlighted a persistent problem facing adolescent girls and boys who leave school for various schools.
