Chris Gard and Connie Yates are appealing a High Court ruling made last month that specialists can move son Charlie to palliative care.
The court heard his parents "wish to exhaust all possible options" and take him to the US for further treatment.
Doctors believe the nine-month-old baby has irreversible brain damage.
Lawyers for Great Ormond Street Hospital told the court the baby is unable to see, hear, make a noise or move.
The parents' barrister, Richard Gordon QC, told the appeal hearing specialists at the hospital were "usurping the parental function" and "seeking to detain Charlie Gard in hospital".
Referring to their hopes of taking Charlie abroad for a therapy trial, Mr Gordon said the pair believed it would cause no "significant harm" to their baby and they did not want to look back and think "what if?".
Lawyers for the parents also argued High Court judge, Mr Justice Francis, did not give enough weight to Charlie's right to life when making his decision.
Charlie, who was born healthy on 4 August 2016, has a disorder called mitochondrial depletion syndrome which affects the genetic building blocks that give energy to cells.
It causes progressive muscle weakness and brain damage.
Lawyers representing Great Ormond Street told the court it was hard for anyone to know whether Charlie is in pain because of the ravages of his illness.
Katie Gollop QC said any further treatment would leave the nine-month-old in a "condition of existence".
During the High Court hearing doctors had argued that continuing life-support treatment would not benefit Charlie but "prolong the process of dying".
Mr Justice Francis agreed and ruled it was in Charlie's best interests for him to be moved to palliative care.
The baby's parents, of Bedfont, west London, have raised more than Â£1.3m to treat their son abroad.
The judgement from the Court of Appeal will be announced on Thursday at 13:30 BST.
The parents of a baby with a rare genetic condition have urged appeal judges not to stand in the way of their "only remaining hope" of his survival.