Tom Evans and Kate James, who are in their 20s and from Liverpool, wanted judges at the European Court of Human Rights (ECHR) in Strasbourg to examine issues relating to the future of their son, Alfie Evans.
But ECHR judges on Wednesday rejected their bid.
A spokesman for the ECHR said judges had declared the application inadmissible and found no appearance of any human rights violation.
The couple had already run out of legal options in the UK.
A High Court judge has ruled that doctors at Alder Hey Children's Hospital in Liverpool can stop treating Alfie, against the wishes of his parents.
That decision has been upheld by Court of Appeal judges and Supreme Court justices.