Sebastian Joshua Grewal underwent a second surgery to relieve pressure on his brain on Tuesday, after recovered in critical condition from Monday's crash in Hesperia, California, The Los Angeles Times reported.
The 47-year-old pilot, identified by Los Angeles Fire Department as Brian Lee, died in the accident.
Lee, a paramedic, was flying the plane carrying Grewal while off duty. Lee died from the injuries he sustained.
Sebastian, who was pulled from the wreckage in critical condition, is described by his father as wanting to be a pilot.
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Grewal described Lee as a beloved friend of his.
Lee, who served more than 25 years with the fire department, was flying Sebastian over El Mirage Dry Lake when the aircraft experienced trouble.
The plane, identified as a single-engine Grumman AA-1A, nosedived into the ground before flipping several times, a spokeswoman for the San Bernardino County Fire Department said.
The crash is now under investigation by the Federal Aviation Administration and the National Transportation Safety Board.