Persistent (adjective)

1. Continuing to exist or occur over a prolonged period of time.
2. Not giving up easily; determined.
3. Refusing to be discouraged by difficulties.

Origin:

From the latin persistere "to persist".

Examples:

1. The persistent rain continued for several days.
2. She was persistent in her efforts to find a job.
3. He was a persistent visitor despite being told to leave.
4. The persistent cough wouldn't go away.
5. Her persistent calls finally convinced him to go out with her.