Possible Clues:

• Persevere, like a museum curator?
• Motto on an inspirational cat poster
• "Don't give up," and a suggestion that can apply to 17-, 25-, 49-, and 59-Across?
• 'Keep up the fight'
• 'Don't give up now!'
• Persevere (slang)
• "Don't give up yet!" ... or a hint to the answers to starred clues
• 'Don't give up yet!' ... or a hint to the answers to starred clues
• ...from a sport climbing coach
• ''Persist!''