Translation of "Persévéré" in English

Mais, ils ont persévéré.

However, they kept on doing their very best.

Grâce à eux, j'ai persévéré.

That's why I would not give up.

De retour à San Diego, j'ai persévéré dans mes efforts

When I got back to San Diego, I continued making more positive changes,

Alors j'ai persévéré, j'ai acheté l'instrument et cherché un professeur.

so I went on, bought the instrument and started looking for a teacher.