Persevering describes a person — or their effort — that keeps trying, in a determined way, even when things are difficult. It comes from the verb persevere, and like that verb it shows approval: a persevering student is one we admire for not giving up. You will also hear it as the -ing form of the verb (“she is persevering with the course”), but in many learner books this word is the describing word. It is a compliment, not a complaint.