Michael Rickman, 11, is in intensive care in the burns unit at Broomfield Hospital in Chelmsford, Essex.
He was injured along with Michael Bonfield, 12, when the mini-motorbike was involved in a collision with a car in Darenth, Kent, on 1 July.
The older boy is out of intensive care and "showing signs of getting better".
Anita Bonfield urged parents whose children had mini-motorcycles to "think twice about letting them ride it or even be a passenger on it".
'Fighting spirit'
Michael Rickman was left critically ill with severe burns after the bike caught fire following the collision.
His mother Lilian said: "It is very difficult to express how I am feeling at this moment in time.
"Michael has a true fighting spirit. He wants to live and he knows I want him to live.
"We are holding on together, helping each other to get through each day."
The 11-year-old's mother said reading to him from a Nanny McPhee book "gives me the courage to keep strong for Michael".
^ Back to top | BBC Sport Home | BBC Homepage | Contact us | Help | ©
~RS~q~RS~~RS~z~RS~21~RS~)