No.

In Jain Dharma there is no religious rule to “keep having sex until a son is born.” Sons or daughters have no bearing on one’s spiritual progress. All souls are equal, and liberation depends on one’s own right faith, right knowledge, and right conduct—not on children or lineage.

What Jain texts actually teach about sexuality:

• For monks and nuns: complete celibacy (brahmacharya mahavrata).
• For laypeople: chastity with restraint (brahmacharya anuvrata), usually expressed as swadara-santosh—contentment with one’s own spouse, avoiding excess and misconduct. Procreation is optional, not a religious duty, and there is no requirement to try for a particular gender.

Both Digambar and Shvetambar traditions agree on these vows. There is no scriptural mandate favoring a male child.

For a simple overview of the Jain vows and brahmacharya, see:

• Twelve vows of a layperson and brahmacharya anuvrat
• Swadara-santosh (contentment with one’s spouse) and brahmacharya