But in an unusual agreement with the drug maker, Janssen Pharmaceuticals, owned by Johnson & Johnson, the drug will be allowed to remain on the market until at least mid-August.
The FDA says that's to give patients time to switch to alternative therapies.
But CBS News Correspondent Sharyl Attkisson reports the decision to leave Propulsid on the market for even a few more months is upsetting some scientists inside the FDA who say it's just too dangerous.
Those FDA sources point to the case of Gage Stevens -- a case they consider especially significant, even though it's still largely unknown to doctors who prescribe Propulsid and thousands of patients still taking it.
Like many infants, Gage Stevens was born with a stomach acid problem called reflux -- it made him uncomfortable and fussy.
When he was three months old, his parents took him to a specialist at Pittsburgh Children's Hospital, Dr. Susan Orenstein.
The baby's mother, Gretchen Stewart, tells CBS News, "She said he definitely does have reflux, do you want to be in the study if you're not in the study and you're being seen with me, he's probably still going to be put on this drug."
The drug was Propulsid.
Approved only for adults, doctors widely prescribe it for children in so-called "off-label use" which is perfectly legal, even though the proper dosage hasn't been clinically established.
That was one point of the study.
Stewart says she was under the impression that the risks of using the drug were "very minimal." She says, "little did I know more or less he was a guinea pig."
Gage took Propulsid for four months.
Then one night last November, he went to sleep and never awoke.
The death of a baby, of anyone in a study, is an important event that must be reported to the FDA, and could influence whether the drug should be withdrawn.
Dr. Orenstein informed the FDA about Gage's death.
It's unclear who, if anyone, should have told Gage's parents that Propulsid could be to blame, but nobody did.
The coroner says he was not told that Gage had been given Propulsid.
Dr. Cyril Wecht, Allegheny County coroner, says, "Based upon our findings known to us at that time, we concluded that it most likely was a case of SIDS, sudden infant death syndrome . we were not given all of the information at that time."
The study consent form made no mention of any deaths associated with the drug under the heading of "risks and benefits," and did not tell parents that Propulsid had been the subject of increasing debate in the medical community over its safety, leading the drug maker to issue a series of revised and more stringent warnings about Propulsid in a form commonly known as "Dear Doctor" letters.
Under a brief section titled "neinformation," the consent form did mention "a few" baby deaths, but said those happened "usually" while the baby was taking a "prohibited antibiotics" with Proupulsid.
Only months after Gage's death, while doing their own research, did Gage's parents discover Propulsid had been linked to dozens of adult heart deaths.
They also discovered that, when Gage entered the study, the FDA had already considered Propulsid a drug of "last resort" that should be used only if all other treatments failed.
That was not the case with Gage.
And the consent form falsely claimed Propulsid had "just been approved by the FDA" for infants.
In fact, the FDA never approved it for pediatric use.
The study director, Dr. Orenstein, refused repeated requests from CBS News for an interview, but answered a few limited questions through a spokesman at Pittsburgh Children's Hospital.
She calls the mistaken statement about FDA approval in the consent form an "oversight."
And she claims parents got the correct information verbally, something Gage's parents dispute.
They didn't even get the printed warning normally issued with prescriptions, they simply got a blank, white box filled with a bottle of medicine that had no warnings on the label.
Stewart says, "It's like giving you chemotherapy for a toothache, it's just the benefits don't outweigh the risks. I mean, it's reflux! It's not something that's (going to kill him)."
Dr. Orenstein first told CBS News that she ended her Propulsid study in March, then later said she ended the study in February when the FDA told her it was investigating a possible link between Gage's death and Propulsid.
On Tuesday, five months to the day after Gage died, the coroner revised the infant's death certificate to reflect that the death was no longer considered SIDS, but instead was due to the medicine he took while in Dr.Orenstein's drug study.
Sources tell CBS News that Dr. Orenstein recently claimed to others that she believed Gage's death was completely unrelated to Propulsid, but would not answer questions about what she thought was to blame.
One FDA source says the fact that the agency is allowing Propulsid to stay on the market for a few more months sends a mixed message to doctors who are still prescribing Propulsid, "like water."
"They know it's coming off the market," said the source, "but they think, 'How bad could it be if the FDA is not taking it off immediately?'" The source also argues, "Propulsid doesn't treat a life-threatening condition, there's no reason to let patients keep taking it and risk more deaths."
FDA officials responded by telling CBS News that doctors consider Propulsid highly effective and want to give their patients time to try other medications before taking Propulsid away from them entirely.
The FDA emphasizes it should only be used on patients for whom all other accepted therapies have failed
As of April 1, the FDA reported Propulsid had been associated with 111 heart-related deaths in adults and children.