Police say all the information they have "suggests that Mike and John have not left the Catlins area".
If the boy is on the run and hiding out with his step-dad, it could "psychologically terrible", according to child and family psychologist David Stebbing.
"Here's a kid who's probably been brainwashed," he said.
The youngster could now be suffering from Stockholm syndrome, or capture-bonding -- a psychological phenomenon in which hostages express empathy and sympathy and have positive feelings toward their captors, Mr Stebbing said.
He could become so reliant on his stepfather that he would struggle to "break free".
If on the run, the isolation meant Mike could become totally severed from all other relationships, inhibiting the boy's social skills, and stunting his academic development.
"There's all sorts of risks to this kid," Mr Stebbing said.
Beckenridge lost a custody battle in February this year after a judge found that the boy had become "alienated" in his care.
The decision came after specialist advice to the court, the judge said, stressing that there was no question of domestic violence.
Mr Stebbing said that children who are alienated from one parent "absolutely" take on the views of the alienator.
Their understanding and rationale for doing so is often "very limited", the child psychologist said.
"This kid is obviously at a pretty important stage of his development, where ... he's still in middle childhood, which means he's going to see things in fairly absolute ways.
"He won't understand nuances in the way that a kid even a couple of years older potentially would."
Some friends and neighbours of Beckenridge believe he faked the deaths and fled New Zealand, possibly to Papua New Guinea.
NZME. News Service today revealed that authorities in PNG, where Beckenridge worked for several years as a helicopter pilot, are aware of a man entering the country in February on a cruise ship using one of Beckenridge's known aliases -- that of 61-year-old Australian passport holder John Locke -- weeks before he snatched the schoolboy.
The Immigration and Citizenship Service Authority are now investigating after the "Mr Locke" appears to have overstayed.
