hartnäckig
persistent
Describes something that is difficult to remove, heal, or solve, such as a stain, an illness, or a rumor.
Dieser Rotweinfleck auf dem Teppich ist wirklich hartnäckig.
This red wine stain on the carpet is really persistent.

persistent / stubborn
Loading your saved state.
persistent
Describes something that is difficult to remove, heal, or solve, such as a stain, an illness, or a rumor.
Dieser Rotweinfleck auf dem Teppich ist wirklich hartnäckig.
This red wine stain on the carpet is really persistent.

The word is a compound of 'hart' (hard) and 'Nacken' (neck) with the adjective ending '-ig'. The idea of a 'harter Nacken' (stiff neck) that cannot be bent figuratively describes the quality of being stubborn, unyielding, or resistant.
Er blieb hartnäckig bei seiner Meinung, obwohl alle dagegen waren.
He stubbornly stuck to his opinion, even though everyone was against it.
In this meaning, 'hartnäckig' (persistent) is often used to describe things that you want to get rid of but that remain. Typical examples are 'ein hartnäckiger Fleck' (a stubborn stain), 'ein hartnäckiger Husten' (a persistent cough), 'hartnäckiger Schmutz' (stubborn dirt), or 'ein hartnäckiges Gerücht' (a persistent rumor).
Ich kämpfe seit Wochen gegen eine hartnäckige Erkältung.
I have been fighting a persistent cold for weeks.
When 'hartnäckig' (persistent/stubborn) describes a person, the meaning can be positive (determined, persevering) or negative (stubborn, unreasonable), depending on the context. The situation and the wording in the rest of the sentence show which evaluation is meant.
Die Journalistin stellte so lange hartnäckig Fragen, bis sie eine Antwort bekam.
The journalist kept asking persistent questions until she got an answer.
chronic
'chronisch' and 'hartnäckig' can both describe something that does not go away quickly. 'chronisch' is used especially for illnesses or lasting negative conditions that have existed for a long time or keep coming back. 'hartnäckig' emphasizes more that something is difficult to remove, heal, or solve. It can also describe a person who does not give up. The words can be confused with complaints such as a cough or pain. In that case, 'chronisch' describes the long-term condition more, while 'hartnäckig' describes strong resistance to treatment or a solution.

Der hartnäckige Fleck auf der Jacke geht auch nach dem Waschen nicht weg.
The stubborn stain on the jacket does not come out even after washing.
Mein Bruder hat chronische Rückenschmerzen und geht regelmäßig zur Ärztin.
My brother has chronic back pain and regularly goes to the doctor.