persistent
per-SIS-tuntadjMeaning refusing to give up; continuing for a long time
Memory hook PER-SISTER-ent: little sister never gives up. Ivy asks her big brother to play catch ten times, twenty times, fifty times, until he finally says yes. Ivy is persistent.
The persistent puppy scratched at the door again and again until someone finally let him in.
In context The inventor’s first forty designs failed, but she was persistent, and the forty-first worked so well that she sold thousands.
Similar determined, tenacious, relentless, constant
Opposite irresolute, fleeting, brief
From Latin persistere, “to continue steadfastly”: per (thoroughly) + sistere (to stand).