The phrase "a particularly vexing problem" is correct and usable in written English.
You can use it when describing a problem that is especially frustrating or difficult to solve.
Example: "The team has been struggling with a particularly vexing problem that has delayed the project timeline."
Alternatives: "an especially challenging issue" or "a notably frustrating dilemma."
Nutrition can be a particularly vexing problem because the caloric needs are often greater than the patient can consume in a normal fashion.
The determination of CERCLA liability for corporate subsidiaries, individual corporate actors, lenders, and others who do not actually own or operate a hazardous waste site has proven to be a particularly vexing problem.
Student debt came next, Taylor said, because it was similarly sympathetic — many people agree that everyone should have access to both health care and education — and because student debt has become a particularly vexing problem.
The thieves pose a particularly vexing problem, officials said, because they pick out the most sought-after trash — clean, neatly bundled cardboard, or heavy pieces of metal — thereby removing the crème de la crème from the city's mix.
Finally, we returned to the science, and I addressed a theme that's come up on this blog, and that I think contributes substantially to making the human response to climate change (or global warming) a particularly vexing problem — the reality that while the basics of the science are clear, the science on questions that matter most to society is not.
The inquiries and analyst's account underscore how e-mail messages, more so than telephone calls, have proved to be a particularly vexing problem for the agency because of technological difficulties in distinguishing between e-mail messages by foreigners and by Americans.
Another particularly vexing problem for advertisers is the way consumers frequently switch back and forth between their mobile devices and a PC when performing a task.
A particularly vexing clinical problem for breast cancer clinicians is the evaluation of response of bone metastases [ 58].
Wear has been an especially vexing problem.
For the Israeli leadership and many of its advocates, the Iran negotiations presented an especially vexing problem of political triangulation.
Starter cultures are a particularly vexing ingredient.
