a vexed question

vexed question

A topic or point that people discuss or argue about at length, but never manage to settle or resolve. After three months of discussions, the vexed question of the disputed border continues to derail peace talks. How the government should go about dismantling the organization is still something of a vexed question.
See also: question, vexed

a vexed ˈquestion

a difficult problem that people often talk and argue about: They’re discussing the vexed question of private health insurance.
See also: question, vexed