Cigars do not have to be smoked in one sitting. A cigar can be set down for short periods (a phone call, a quick errand, a refill) and relit without consequence. Within an hour or two, the smoke is essentially unchanged.
Beyond about two hours, the picture changes. The internal moisture of the smoked portion begins to dry out, the residue of combustion settles into the wrapper, and the relit smoke takes on a stale, slightly sour character that does not match the cigar’s profile. By the next day, the cigar is no longer worth relighting; what is left is best discarded.
The technique for a clean relight: tap any soft ash off the foot, then re-toast the cigar exactly as you would when first lighting it. Hold the foot just above the flame at a forty-five degree angle, rotate slowly until the entire perimeter glows, then puff gently with the foot in the flame. Do not skip the toast; an unfresh foot lit cold produces harsh smoke from the relight.
If the cigar has been out for an hour or so and you are about to relight, blow gently through the cigar from the head end first. This clears stale smoke from the inside and produces a cleaner relight.
For more on cigar fundamentals, see The Anatomy of a Cigar.