To date, authorities have recovered 51 bodies as well as 600 pieces of wreckage from the Airbus A330-200 jetliner.
Experts say the black boxes may be key to deciding what brought the airliner down, but signals from the voice and data recorders begin to fade after about 30 days.
"We'll have a better idea on July 1 on how much longer we'll go," Willie Berges, the Brazil-based commander of the US military forces supporting the search, said.
Berges said searchers were likely to keep going 12 to 15 days past the 30-day mark of the crash.
A French nuclear submarine and two French-contracted ships towing US navy listening devices are patrolling a search area with a radius of 80km off Brazil's northeastern coast where it is believed the plane descended.
The black boxes send out an electronic tapping sound that can be heard up to 2km away.
With the recorders still missing, accident investigators have focused on automated messages sent by the plane minutes before it lost contact.
One indicates the plane was receiving incorrect speed information from external instruments, which could destabilise the plane's control systems.
Experts have suggested those external instruments might have iced over.
Air France has now replaced the monitors, called Pitot tubes, on all its Airbus A330 and A340 aircraft.
On Thursday, US safety officials said they were investigating two incidents in which airspeed and altitude indications in the cockpits of A330 planes may have malfunctioned.
The aircraft are the same type as the Air France plane that crashed.
In both cases the planes landed safely, and no one was injured, the National Transportation Safety Board said in a statement.