There are several synonyms for the phrase "holding out hope." One alternative is "clinging to optimism," which suggests a persistent belief in positive outcomes. Another option is "maintaining faith," which conveys a sense of trust in a higher power or other supportive forces. "Persisting in expectation" implies a determined expectation that things will turn out well. "Sustaining a positive outlook" emphasizes the importance of maintaining a hopeful mindset in the face of adversity. Finally, "preserving hope" suggests a steadfast commitment to maintaining a sense of hope, even in difficult circumstances. Regardless of the specific synonym used, all convey a sense of determination and positivity in the face of uncertainty.