Only his tenacious grip enabled him to hang onto the sheer cliff face.

The word "tenacious" in this context refers to a strong grip or determination to hold on firmly. Therefore, "persistent" is the most fitting synonym, as it conveys a sense of unyielding strength and determination. The character's ability to cling to the sheer cliff face relies on his unwavering grip, which aligns with the idea of being persistent in maintaining that hold.

In contrast, "lively" does not capture the seriousness or strength implied by "tenacious." "Fragile" suggests weakness and vulnerability, which directly contradicts the idea of a strong grip. "Complicated" relates to intricacy and difficulty, which does not resonate with the straightforward concept of holding on firmly.