PORTLAND — A Kittery businessman facing a prison sentence for falsely declaring on a Small Business Administration loan application that he had no criminal past has lost his bid for a new trial.

Peter Enzinger, 44, was convicted last month in U.S. District Court for knowingly making false statements about his criminal record. Under federal sentencing guidelines, he would face up to two years in prison.

Three days after the trial, a juror wrote Judge D. Brock Hornby a letter saying that he or she misunderstood the need to reach a unanimous verdict. The juror wrote that he or she believed Enzinger was innocent but thought that the other 11 other jurors needed to be convinced for Enzinger to be acquitted.

Hornby this week denied Enzinger’s request for a new trial, writing that a juror’s misunderstanding of the judge’s jury instructions is not grounds for overturning a verdict.

In March 2009, Enzinger applied for the $1.3 million loan on behalf of his businesses, Kittery-based Atlantic Medical Supplies and Seacoast Sleep Solutions. A form submitted as part of the application indicated that he had never been charged with, arrested for or convicted of any criminal offenses other than minor motor vehicle violations. But Enzinger had four convictions in Massachusetts under the surname Shays.

During the trial, the defense suggested that a staff person may have filled out the form. Enzinger also testified that he had been issued “tickets” for 1997 incidents of shoplifting and being a disorderly person but didn’t realize they were criminal convictions. He claimed he had no memory of the other two incidents that resulted in convictions for furnishing liquor to a minor in 1987 and disturbing the peace in 1990.