A new oath holds pretty well; but... when it is become old, and frayed out, and damaged by a dozen annual retryings of its remains, it ceases to be serviceable; any little strain will snap it.

Twain treats an “oath” (a solemn promise, often a moral resolution) as something with a material lifespan: it works when fresh, but repeated reuse and ritual recommitment (“a dozen annual retryings”) wear it down until it becomes brittle. The image satirizes the way people rely on periodic vows—New Year’s resolutions, temperance pledges, reform promises—as substitutes for sustained change. By likening moral commitment to a fraying rope that will “snap” under “any little strain,” he suggests that virtue grounded mainly in ceremony or self-dramatization is structurally weak. The line is both comic and skeptical: it implies that character is proven in ordinary pressures, not in grand declarations.