This instinct is much like the sulfur on a kitchen match. When you strike it against the phosphorous on the matchbox, it will ignite into flame. It gets very hot very quickly. It flares up for a second or two, long enough to light the wood of the match. However, that flame wasn’t designed to last. If the match is wet, the flame will soon flicker and die. It was only created to be a catalyst to start the fire, not to keep it going.
The instincts Hashem put into man will cause him to care for his offspring when they are young and in need of great attention, but that sense soon fades. If the person is a giving, caring individual, that initial burst will be enough to be the catalyst to real attachment, and the bonding will continue and deepen as the flame of love grows. If the wood is wet or rotten, the flame will weaken and go out.
This seems to be the answer to the question. The heart of the tzaddik is pure and is filled with love and affection. Sarah worked on herself to such an extent that she was completely other-centered. Her whole existence was focused on helping others, taking care of their needs, and doing for them. When she had her own child, the natural maternal instinct flared and caused a bond and attachment to her child that was unbreakable. But that sense didn’t fade as the years passed.
Because her heart was so pure, it increased and became more powerful so that she and Yitzchak were as one – to such an extent that when she heard the news that her precious child was in pain, the thought was too much for her to bear, and she died.
This concept has powerful ramifications in our own lives. For parents to become true advocates, protectors, guides, and mentors to their children, they must foster this bond and allow it to grow up with their child. The instinct will only take them so far. After a point, it is their own dedication and devotion that takes over and creates the true bond. While we will never reach the level of the Avos, they are guiding lights to show us the dynamics of the human personality and the heights a human can aspire to.