The legal team of the former pop star, real name Paul Gadd, argued media coverage had made a fair trial impossible.
But three judges said there was nothing "unsafe" about the conviction.
The 71-year-old was jailed for 16 years in February for offences at the height of his fame, between 1975 and 1980.
He had denied the allegations against him.
A jury at Southwark Crown Court found him guilty of one count of attempted rape, one of unlawful sexual intercourse with a girl under 13, and four counts of indecent assault.
At his sentencing, Judge McCreath told him his victims were "profoundly affected".
He said the offence of attempted rape was "so serious" as to justify the maximum available sentence.
Gadd was jailed in Vietnam in 2006 for molesting two girls aged 11 and 12.
He later became the first person to be arrested under Operation Yewtree, the investigation launched by the Metropolitan Police following the Jimmy Savile scandal.
Disgraced singer Gary Glitter has lost a Court of Appeal challenge against his conviction for sexually abusing three young girls.