persistent
US /pɚˈsɪs.tənt/
UK /pɚˈsɪs.tənt/

1.
continuing firmly or obstinately in a course of action in spite of difficulty or opposition
:
•
She was persistent in her efforts to learn English.
•
His persistent questioning eventually led to the truth.
2.
(of an unwanted phenomenon) continuing to exist or occur over a prolonged period
:
•
The persistent cough kept him awake all night.
•
We need to find a solution for this persistent problem.