Momberg was found guilty on four counts of crimen injuria for racially abusing a police officer in 2016.
The attack was caught on camera, sparking outrage across the country.
The National Prosecuting Authority has welcomed Wednesday's ruling in the Randburg Magistrates Court.
“As the NPA, we are glad that the court ruled that there are no prospects of success on the appeal because as the State, it is a fact that we managed to prove our case beyond reasonable doubt.”
This article first appeared on EWN : Convicted racist Vicki Momberg loses bid to appeal sentence