The 11-year-old boy disappeared from his Invercargill school after Mr Beckenridge picked him up on March 13.
At the time Mr Beckenridge had a parental order in place against him.
Police had been searching Curio Bay in Southland since pieces of Mr Beckenridge's car washed up last week.
An underwater camera had earlier pinpointed where the dark blue Volkswagen Touareg was lying, at the bottom of a 90m cliff.
However, conditions have been too rough to bring it onshore.
Police spokesman Nic Barkley said the car would not be recovered today, and likely not tomorrow either.
"Where the car is, there are big swells and we need to wait for it to die down. Then we can look at the best options of getting the car out," he said.
The main focus of the investigation was the vehicle, police said.
Mr Barkley said officers were still working through information it has received from the public.
"They are working through a number of different inquiries," he said.
Police have carried out land searches and inquiries into where the pair might be.
Michael left James Hargest College's junior campus during a lunch break with his stepfather.
The school's principal Andrew Wood said it was "perfectly possible" for a student to leave the school unnoticed.
Mr Beckenridge is also known as John Robert Lundh, Knut Goran Roland Lundh or John Bradford.
Michael is of solid build and of Asian descent. Mr Beckenridge is 1.75m in height, of medium build and of Swedish descent.
Anyone with information that might assist in locating the pair should contact the Southern District Command Centre on 03 471 5002.
Information can also be provided anonymously to the Crimestoppers organisation on 0800 555 111.
