Mr Evans and Ms James had battled to have his care transferred to a hospital in Italy and for his life support not to be switched off.
At the appeal hearing, Lord Justice Davis said doctors had agreed that there was "no hope" for Alfie.
The case ultimately revolves around the question of whether parents have the right to make healthcare decisions for their children.
Alfie's Army - as supporters call themselves - say the protests are peaceful and asked on its official Facebook page for demonstrators to be "respectful" to the hospital. He argued that it was a deprivation of Alfie's liberty in not letting him travel to a different hospital.
Alder Hey Children's Hospital say continuing to treat Alfie was "unkind" and "futile" but his parents Tom Evans, 21, and Kate James, 20, from Bootle, Merseyside, want to take him to a hospital in Rome and say they have a private ambulance and jet on stand-by.
The judge said doctors at the hospital all believe that the sick tot "could not be saved".
In his ruling today, Lord Justice Moylan repeated the arguments made recently by Lord Justice Hayden about the baby's care.
Mr Justice Hayden set a date for the 23-month-old, who is being cared for at Alder Hey Children's Hospital in Liverpool, to be allowed to die.
The justice stated that the parental rights of Tom and Kate over Alife "do not take precedence".
'We will never give up on you Alfie'.
In addition, Moylan said it is "wrong to say that the parents' own views can trump that judicial determination", according to LifeSiteNews.
"As has been determined with considerable clarity in this case, Alfie's best interests are determinative and the court has decided what treatment he should or should not receive".
Mr Evans emerged from the hospital two hours after the decision was given by the court in London. He is on life support at Liverpool's Alder Hey Children's Hospital which is part of the UK's National Health Service Foundation Trust.
In February the High Court ruled doctors could stop his life support.
Judges have heard that Alfie, born on May 9 2016, is in a semi-vegetative state and has a degenerative neurological condition doctors had not definitively diagnosed. Courts have refused to allow the parents to determine what is in Alfie's best interest.