In our current age any physician would be aghast at such early motherhood; but the Tudor royal marriages were dynastic. People were certainly more fatalistic, and death in childbirth was no stranger to any family. Everyone knew someone, or was related to someone who had died in the birthing bed. It seems the fear of early childbearing, in Tudor days, was that a woman would permanently lose her figure if she bore children at such a young age. It may be possible that Margaret did sustain some injury, since she was married a total of 4 times, and never again bore a child after her son Henry.
Margaret Beaufort was an exceptionally pious woman, and her son Henry had a great respect for her. Margaret rose from bed at midnight to attend the Matins of the friars. She spent mornings in her chapel, and typically wore a St. Francis habit beneath her robes. Margaret kept a yearly Maundy, a practice which Catherine of Aragon would imitate. This was the old custom of royal persons washing the feet of the poor, and after this distributing a purse of money to those unfortunates. (Anne Boleyn would also keep the practice of the Maundy. And some recipients noted that she was more generous in her distribution than had been Queen Catherine.)
For generations thereafter, Margaret Beaufort Countess of Richmond would be considered a fine example of piety, and of a new tradition of learning and study for women.