Why did not Shri Rama and Sita have children during the 14 years period of exile?

 

 Kaikeyi asked King Dasaratha to redeem the two boons he had granted her long ago.

अभिषेकसमारम्भओ राघवस्योपकल्पितः || २-११-२४
अनेनैवाभिषे केण भरतो मेऽभिषिच्यताम् |

"All arrangements have been made to undertake Rama's coronation. Let my Bharata instead be coronated on this occasion itself".

नव पञ्च च वर्षाणि दण्डकारण्यमाश्रितः || २-११-२६
चीराजिनजटाधारी रामो भवतु तापसः |

"Rama has to take refuge in the forest of Dandaka for fourteen years and let him become an ascetic wearing rags, deer skin and matted hair".

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So, Kaikeyi desired that Shri Rama should live in the forest like an ascetic wearing appropriate dress and with matted hair. It indicates that Shri Rama should abstain from sexual activities, during the 14 years period of exile.

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Further, when he revealed this issue to Sita and directed her to remain in Ayodhya, while he will proceed towards the Forest, Sita insists following him and states as follows:.

भर्तुर् भाग्यम् तु भार्या एका प्राप्नोति पुरुष ऋषभ |
अतः चैव अहम् आदिष्टा वने वस्तव्यम् इति अपि || २-२७-४

"Oh, Rama the best of men! Wife for one gets fortune of the husband. For that reason, I am also destined to dwell in the forest."

शुश्रूषमाणा ते नित्यम् नियता ब्रह्म चारिणी |
सह रंस्ये त्वया वीर वनेषु मधु गन्धिषु || २-२७-१२

"Oh, brave man! performing service to you regularly, having the necessary discipline, observing chastity, I would like to stay with you in the forests which smell like honey."

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Hence, Sita also decided to follow him in letter and spirit, ie., she will follow him like a shadow and abstain from sexual activities (रंस्ये नियता ब्रह्म चारिणी).

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Hence, when both husband and wife decided to remain as ascetics, there is no question of begetting children during the 14 years exile period.