persevering

(verb) be persistent, refuse to stop. Synonyms: persevere, persist, hang in, hang on, hold on. Examples: "He persisted to call me every night." "The child persisted and kept asking questions."

(adj) quietly and steadily persevering especially in detail or exactness. Synonyms: diligent. Examples: "A diligent (or patient) worker." "With persevering (or patient) industry she revived the failing business."