Santhana Gopala form of Vishnu is associated with a famous story involving Sri Krishna and Arjuna. Arjuna was filled with pride after the Kurukshetra war. He thought there was no one to defeat him on earth and he could solve all problems with his bow and arrow. Sri Krishna decided to kill the pride of Arjuna.
A Brahmin couple in Hastinapura had the bad luck of losing eight children during childbirth. All children died when they were just born.
The Brahmin approached Arjuna who promised that nothing will happen to the ninth child and that he will stop Yama from reaching the child.
Arjuna stood guarding the house when the wife of Brahmin was delivering the ninth child. But the ninth child too died. An angry and sad Brahmin scolded Arjuna for his inability to protect the child. Arjuna then promised that he will save the 10th child and if he is unable to save the child then he will self immolate.
When the Brahmin wife was getting ready to deliver the 10th child, Arjuna created a wall with divine arrows around the house of the Brahmin. But after delivery the child disappeared.
Arjuna then went searching for the child in all directions. He finally reached the abode of Yama. But Yama told that he had nothing to do with the incident as the death time of the child had not yet arrived.
Arjuna returned back to the Brahmin and accepted his inability to find the child. Arjuna decided to end his life by jumping into fire.
Suddenly Sri Krishna appeared there and took Arjuna with him to the seven storied Vaikunta guarded by Jaya Vijaya. Here he saw the nine children of the Brahmin couple playing with Mahavishnu and Lakshmi Devi. The tenth child was sitting on the lap of Mahavishnu.
Arjuna lost his pride and realized that there were many things beyond his capacity. He asked for forgiveness and returned to earth with the 10 children of the Brahmin couple.
The form of Vishnu sitting with 10th child is the Santhana Gopala form of Vishnu and this form is worshipped in temples in South India, especially in Kerala.
It is believed that worshipping this form of Vishnu will help in solving all kinds of pregnancy and childbirth related problems.