The House voted several times against a Democratic-led attempt to bring to the measure to the floor. The resolution was largely symbolic and would carry no legal weight with the U.S. attorney's office or FBI.
Its supporters want the Justice Department to look into whether the three-year probe of allegations against the former Penn State assistant football coach took too long and put children's safety at risk.
Sandusky plans to appeal his conviction after being sentenced last week to at least 30 years in state prison for sexually abusing 10 boys. The scandal led to the firing of longtime coach Joe Paterno and criminal charges against two Penn State administrators for allegedly failing to properly report suspected child abuse and perjury.
Penn State confirmed federal prosecutors have sought a wide range of Sandusky-related materials from the university, but the target and nature of that investigation are unclear.
"In fact, an FBI investigation is taking place, coincident with the work that is being done by the attorney general's office," said Majority Leader Mike Turzai, R-Allegheny, during floor debate.
Democratic Whip Mike Hanna, D-Clinton, said it was "absolutely inexcusable" that Republican leaders had canceled the final two days in November of the current two-year legislative session, leaving too little time to bring up discharge resolutions.
"This resolution is about protecting Pennsylvania's children," Hanna said. "Nothing should be more important to the members of this body."
The issue has clear political overtones. The Sandusky investigation began under Republican Gov. Tom Corbett, when he was attorney general. The pace of the investigation, which did not become public until after he was sworn in as governor, has been a topic of much criticism and speculation.
Corbett has said the amount of time was needed to ensure prosecutors would be able to secure a conviction, while critics have said child molestation cases normally do not take nearly as long as Sandusky's did.
Sandusky, 68, was arrested in November and convicted in June of 45 counts of child sexual abuse. Corbett's office has repeatedly pointed to that verdict as vindication of decisions made during the investigation.
The resolution, introduced in December, called for the federal government "to completely investigate why the Office of Attorney General took so long to investigate this matter and to finally take action to remove Mr. Sandusky from further contact with minors."
The trial of Tim Curley, the school's athletic director on leave, and Gary Schultz, a retired university vice president, is scheduled for January in Harrisburg. Both men have repeatedly denied the allegations against them.