Some yuccas will not become soft regardless of how long they are boiled. In the Dominican Republic they are called "yucas jojotas". They are usually fine to eat and tend to be sweet, but won't become soft as other roots. If most of the roots you are boiling are soft but one or two pieces are jojotas, consider the batch ready to eat.
Left overs can be reheated in slightly salted boiling water or pan fried with cooking oil over medium temperature.