This legal dispute is just one of a number of highly public British cases where parents and doctors have argued over who is more qualified to make decisions regarding a child's medical treatment.
This has led to a debate about whether there is a better way to resolve such disputes outside of the courts.
Archie was found unconscious in his home with a ligature covering his head. His parents suspect he was taking part in an internet challenge that went wrong.
"The events over the past few weeks have raised many important issues, including questions about how death is defined and decided upon.