persist, remain, pursue; see continue 1, endure 1.
To be steadfast
stand firm, insist, be obstinate, stick to one's guns, not take "no" for an answer, hold one's ground.
See persevere in Webster's New World Roget's A-Z Thesaurus II
To continue without halting despite difficulties or setbacks:
To take and maintain a stand obstinately:
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