The phrase "perpetual problem" is correct and can be used in written English.
You can use it to refer to a problem that seems to never go away or to persist over a long period of time. For example, "Climate change is a perpetual problem that we must address."
For drivers, parking is a perpetual problem, especially around the 50th Precinct station house.
The portrayal of teenagers onstage is a perpetual problem in the theater.
In response, despite continuing worries over internal stability and the perpetual problem of a hostile Pakistan, Indian planners have begun to broaden their strategic horizons.
Secondly, the elite decision makers are simply not producing products that America wants — a longstanding and perpetual problem that is visible even outside of cultural industries.
Instead of festering as a perpetual problem this season, the offensive line, like some other parts of the team, has steadily developed.
EXTRA POINTS The Giants Stadium field, a perpetual problem last season, was in terrible shape after a heavy rain began to fall at game time.
Cameron said NATO troop capacity was "patchy" and there appeared to be perpetual problems with shortages of air transport support.
It "also pinpoints the perpetual problems of the judiciary which affect the credibility of the system as a whole and Romania's credibility as well".
The perpetual problems of relatively low salaries and tough working conditions have been exacerbated by a wave of retirements and by a strong economy, which has lured prospective teachers into the private sector.
Unfortunately, we pick people who are not as perfect as we are, so relationships work if you have wound up with perpetual problems you can learn to live with". -- Dr. John Gottman, Author and scientific expert/researcher on marriage, relationships and family.
It is about respectfully hearing the other person when perpetual problems come up.
