By Jonathan Stempel

(Reuters) - A federal appeals court on Wednesday rejected a bid by two former Iowa egg industry executives to throw out their three-month prison sentences after their company Quality Egg LLC caused a nationwide salmonella outbreak in 2010.

By a 2-1 vote, the 8th U.S. Circuit Court of Appeals in St. Paul, Minnesota said prison time was appropriate for Austin "Jack" DeCoster and his son Peter for negligently failing to prevent the outbreak, which sickened thousands.

The DeCosters pleaded guilty in June 2014 to selling contaminated food across state lines, a misdemeanor.

Federal guidelines recommended up to six months in prison, but the DeCosters said no time was appropriate because they had not known their eggs were contaminated at the time of shipment.

Writing for the majority, however, Circuit Judge Diana Murphy said the three-month terms were "relatively short" and did not violate the DeCosters' due process rights, and the convictions did not gravely damage their reputations.

"Congress recognized the importance of placing the burden on corporate officers to protect consumers who are wholly helpless from purchasing adulterated food products which could make them ill," Murphy wrote. "The public has a right to expect a heightened degree of foresight and care."

Wednesday's decision upheld punishments imposed in April 2015 by U.S. District Judge Mark Bennett in Sioux City, Iowa.

Circuit Judge C. Arlen Beam dissented, finding no proof that the DeCosters were negligent or "infected with a guilty mind."

Lawyers for the DeCosters did not immediately respond to requests for comment. The U.S. Department of Justice did not immediately respond to a similar request.

Once among the nation's largest egg producers, Quality Egg paid a $6.79 million fine in the case, after pleading guilty to charges including selling mislabeled eggs and bribing a U.S. Department of Agriculture inspector.

The U.S. Centers for Disease Control and Prevention has linked 1,939 illnesses to the 2010 outbreak, and estimated that 56,000 people may have been sickened.

Murphy said an August 2010 inspection of Quality Egg operations in Iowa uncovered live and dead rodents and frogs in laying areas, feed areas and conveyor belts, as well as outside.

The cases are U.S. v. DeCoster, 8th U.S. Circuit Court of Appeals, Nos. 15-1890 and 15-1891.

(Reporting by Jonathan Stempel in New York; Editing by Tom Brown)