It was the last piece of advice Thomas and Amanda Stansel wanted to hear. But their fertility doctor was delivering it, without sugarcoating.

Reduce, or you will lose them all, he told them.

For more than a year the Stansels had been relying on Dr. George Grunert, one of the busiest fertility doctors in Houston, to produce his industry’s coveted product  a healthy baby. He was using a common procedure called intrauterine insemination, which involved injecting sperm into Mrs. Stansel’s uterus after hormone shots.

But something had gone wrong. In April, an ultrasound revealed that Mrs. Stansel was carrying not one but six babies, and Dr. Grunert was recommending a procedure known as selective reduction, in which some of the fetuses would be eliminated.

The Stansels rejected Dr. Grunert’s advice and, since then, their vision of a family has collapsed into excruciating loss: the deaths of four children after their premature births on Aug. 4, including one who died late Sunday night. The two other infants remain in neonatal intensive care, their futures uncertain.