He persisted in the experiment until he was successful.
Wrong translation… 固執する is used only when a person is so stubborn that he cannot accept constructive criticisms from others or look for better solutions. But the English sentence suggests that he (a scientist, perhaps) is so devoted. That’s a good characteristic.
My alternative translation is:
根気よく is an adverb, and 根気よく続ける means “strive perseveringly”. 根 means “a root”, so a person who has a strong commitment is regarded as having a robust (mental) foundation.
If you want to memorize the term 固執する, here are different example sentences:
プーチン大統領はウクライナ併合に固執し、戦争を続けている。= President Putin is so stubborn that he keeps fighting for the annexation of Ukraine. (Note: I’m posting this comment on April 11th, 2022. The war is ongoing…)
株主からの助言を無視し、社長は当初計画に固執した。= The CEO ignored advice from stakeholders. and he stuck strongly to the initial plan.
As you can see, 固執する has a negative meaning.