persistent

adjective
  1. Continuing to exist or endure over a prolonged period. adjective
    The persistent rain lasted for several days, causing floods in the area.
    Despite the persistent rumors, the company denied any plans to merge.
  2. Continuing firmly or obstinately in a course of action in spite of difficulty or opposition. adjective
    Her persistent efforts eventually led to a breakthrough in the research.
    He was persistent in his attempts to secure a meeting with the CEO.