The battery on the feeding system of a five-year-old boy with a brain tumour who was taken from hospital by his parents without consent is "now likely to have expired", police said.
Ashya King's family took him from Southampton General Hospital at around 2pm yesterday and travelled on a ferry to France some two hours later.
Hampshire Constabulary were told by the hospital that the youngster was missing at 8.35pm last night - more than six hours after he was taken by his parents, Jehovah's Witnesses Brett King, 51, and Naghemeh King, 45.
Assistant Chief Constable Chris Shead said tonight: "Within the last hour, we have been told by medical experts that the battery life on the machine that administers his food is now likely to have expired.
"We don't know whether the King family have any spares, the knowledge, or any way of recharging the battery. If they don't, without properly administered food, Ashya's condition will deteriorate very quickly."
Mr Shead added: "With each hour that passes our concern for him grows."
Earlier Mr Shead said Ashya's health would "deteriorate rapidly" if he was not found.
Police had warned that the battery-operated feeding system would run out of power today.
The youngster is in a wheelchair and is fed through a tube. He has undergone "extensive surgery", with his last operation seven days ago.
"Time is running out for this little boy. We need to find him and we need to find him urgently," Mr Shead told a press conference.
Tonight he warned that the family could have reached other countries beyond France by now.
He added: "There have been widespread media alerts across Europe, focusing on countries where the Kings had a known association; and in particular we continue to work closely with French authorities.
"The last positive information we had placed them in France, but by now we cannot be certain they have not moved on. Our inquiries are totally focused on establishing where they are now. There is still time to find Ashya and make sure he gets the medical help he urgently needs, but we need the public's help to do this."
The Kings boarded a cross-Channel ferry from Portsmouth to Cherbourg with Ashya's six siblings at 4pm yesterday and arrived in France at 8pm local time.
The family, who live in Southsea, are travelling in a grey Hyundai I800 Style CRDI, registration KP60 HWK.
Ashya is likely to be in a wheelchair or buggy, he cannot communicate verbally and is immobile, a police spokesman said.
Mr Shead said the six-and-a-half-hour gap between Ashya being taken from hospital and police being called would be considered "further down the line".
University Hospital Southampton NHS Foundation Trust said Ashya was allowed to leave the ward under his parents' supervision and hospital staff raised the alarm when the length of his absence "became a cause of concern".
The Office of Public Information for Jehovah's Witnesses confirmed that Ashya's parents were followers of the religious movement.
Although Jehovah's Witnesses refuse blood transfusions on religious grounds, a spokesman said there was "absolutely no indication" that the family's decision was "motivated by any religious convictions".
Police have said their "total focus" is on finding Ashya and his parents are not under criminal investigation.
Ashya's paternal grandmother, Patricia King, said his parents were "wonderful" and had been left beside themselves at their child's plight.
Speaking from her home in Southsea, she said of her son: "He's the most caring and wonderful father you could ever have. The kids love him."
She also praised her daughter-in-law, saying she had kept a bedside vigil while Ashya was in hospital.
"We are a very close family," she added.
Ms King said she last spoke to her son "quite a while ago", adding: "He wouldn't have told me anything because he wouldn't want me to know anything in case I got involved in it all."
She said she did not know whether Ashya's illness was terminal, saying: "I knew he was seriously ill, we all knew that."
In a Facebook message posted on July 31, Ashya's brother, Naveed, said the youngster had been diagnosed with a malignant stage four brain tumour.
Naveed - whose Instagram profile says he is 20 - also posted an update on Facebook on August 18 signed "King family", saying that Ashya had been "progressing slowly but continuously with only minor problems along the way".
The post included several pictures, one showing Ashya with his mother and another of a large stitched wound at the back of the boy's head and neck.
Legal experts said that it was "unlikely" that the Kings had committed an offence by taking Ashya out of hospital.
Professor Penney Lewis, of King's College London, said: "I think it is possible that if they are found and still won't co-operate that social services could become involved and the child taken into foster care.
"But if it's just about one treatment - a blood transfusion - the court can address that without changing anything in relation to the care of the child.
"Parental responsibility for the child would remain with the parents but the court would consent to the blood transfusion. Usually this is how matters are resolved."
The academic said there was a "theoretical possibility" that the police and CPS might act against Ashya's parents if any harm came to him because he had been taken out of hospital.
But she added: " There has never been a case where parents have done something like this and they have been prosecuted."