The conviction of 86-year-old Anthony Marshall, the son of late philanthropist Brooke Astor, will stand.
The judge denied a motion to overturn the convictions of Marshall and Astor's former estate lawyer, Francis X. Morrissey.
The men were convicted of exploiting Astor's dementia to steal millions of dollars from her.
Defense lawyers say a juror went along with the guilty verdict because she felt intimidated.
Marshall and Morrissey were sentenced to three years behind bars, but are free on bail pending appeal.
Astor, who died in 2007 at the age of 105, gave nearly $200 million to charity.