SACRAMENTO (CBS13) — A federal judge is giving a Vacaville family more time to fight for their son determined brain-dead.

For 6 weeks, 2-year-old Israel Stinson has been hooked up to a ventilator and his parents have been fighting to keep him on life support.

“He’s alive, he’s definitely still alive,” said his mother Jonee Fonseca.

Jonee and Nate Stinson said their son suffered a brain injury following an asthma attack that left him without oxygen for 40 minutes.

Doctors at UC Davis declared Israel brain-dead and shorty after he was transferred to Kaiser in Roseville where two other doctors made the same determination.

“Unfortunately it’s an irreversible condition, so there are ethical and medical concerns when you consider doing additional procedures on a patient who sustained brain death,” said Dr. Angelica Ha, a Pediatrician at Kaiser.

But over the last few weeks, Jonee said her son has made improvements.

“Now not only is he responding to our touch and our voice, but I’ve seen him take breaths off the ventilator, it’s very hopeful and a good feeling,” said Jonee.

A neonatologist from Ohio said he’s examined Israel and believes he could recover with treatment.

“It’s helped to maintain his life, but somewhere in this United States there’s got to be a doctor who will stand up and treat him,” said Dr. Paul Byrne, President of Life Guardian Foundation in Ohio.

Kaiser argued in court they’ve done all they can and say it’s now for a judge to decide.

“We can use heroic measures and we can use artificial mechanical support to make the heart and lungs function for a certain amount of time, but it’s a limited amount of time,” Dr. Ha said.

As that time grows near, Israel’s family is praying for a miracle.

“I do feel like it’s getting harder, but we made it this far and made it farther than anyone else. I believe that God is with us and we are going to keep pushing on,” said Nate.

The federal judge will likely decide later this week, but either way the family plans to appeal.

Their main concern is finding a hospital that will take their son even with the brain death declaration, which will be incredibly difficult.