I don't know what happens, The plane just disappears when it is over the water. It seems It only happens in the southern Hemisphere. You need to go to one of those real time airplane tracking web sites. Mark Sargent thinks they turn off the GPS tracking for planes in the southern Hemisphere. You should go to his site and check it out.
First let us get one thing clear: GPS satellites transmits data. They do not receive data from airplanes. So for a plane to let others know its position it has to have some way of communicating that. One way of doing that is called ADS-B http://planefinder.net/about/ads-b-how-planefinder-works/
ADS-B requires a ground based antenna. Let us assume that this antenna only reaches a few 100 miles. Then you will lose contact with the plane when it is more than the few 100 miles away from land. In the northern hemisphere there are loads of small islands that could have their own ground based antenna. And since there is more traffic there is probably an incentive to put antennae there to get full coverage. This might not be the case in the southern hemisphere.
To me that is a more likely explanation than "turning off GPS tracking". So if I was really interested, I would do some research on where these ground based antennae are placed and see if that indeed explains it. Keep us posted if you do that.
Just a little review on the air traffic control system. If any thing proves that the earth is a globe it is the factors involved in the radar systems.
This a condensed version of how it works in the USA:
First the air craft is under the control of the airport as it leaves or enters the airport's area of control. The range of the radar is dependent on design criteria of the radar including limitations due to the curvature of the earth.
Once the aircraft leaves the airport's area of control it is "handed off" to an Air Route Traffic Control Center which has computers to track the aircraft. The aircraft have "transponders" which send back information for the controller's radar screen to show the aircraft identification , altitude, speed, etc. (GPS does not do the tracking.)
The radar information is supplied from long range radar systems, again depending on design and distances according to the curvature of the earth. An Air Route Traffic Control Center may have several radars feeding information. The radars may be several hundred miles from the ARTCC's.
On some systems the information was relayed by microwave repeater stations. Again the curvature of the earth is involved.There might be several of these repeaters between the radar station and the ARTCC. Again these stations are spaced according to the maximum distance according to the curvature of the earth.
Also each controller may only control a small area. The ARTCC controls many "sectors" and again one sector may hand off an aircraft to an adjacent sector as the aircraft continues to its final destination.
It does seem a bit complicated when a short explanation is attempted.
But the basic point is that the curvature of the earth plays a big part in air traffic control. Why ?
Because the earth is a globe.
If the earth was flat, in the USA there would be no need for so many ARTCC's , so many radar stations and so many microwave repeater stations. But the earth is a globe and the system works that way and has to be designed accordingly. Why ?
Because the earth is globe.
Also the range of the radios used for communication between pilots and controllers is limited by the curvature of the earth. There is also the need for ARTCC to aircraft communications. Spacing of remote transmitter-receiver stations and means to relay the information is required. Again, what is involved ? The curvature of the earth.
Why ? Because the earth is a globe.
If only the FAA would have hired some flat earth scientists and engineers, the air traffic control system wouldn't have had to be so complicated ! LOL.