There is very little on this transmission you can do/diagnose yourself, so what we would want to do before anything else is make sure the transmission fluid is in normal range, measured with the engine fully hot and running.
If the fluid level is normal then we are going to be relying on getting it on a scan tool to see what is forcing the fail safe mode. Whenever the vehicle locks into 3rd gear, this is fail safe, enacted by the computer to try to protect itself. It saw something on one of the sensors that it either could not interpret or interpreted as dangerous and opted to lock the system down. When this happens, a trouble code is set in the transmission controller (different from the OBD codes, though they may be useful if there are any set).
Given that it is not happening until 3rd gear we can pretty safely rule out all of the speed sensors.... since a speed sensor problem would be evident in any gear not just one in particular.
With 3rd gear using under drive clutch and over drive clutch to engage, we can pretty safely rule out the under drive clutch and solenoid and valve, as they are also used for 1st and 2nd gear as well which again are working normally.
That would leave us with the over drive clutch to be suspicious.... and since fail safe works for third gear (bypassing electronics), that lets us know that the over drive clutch frictions and valve are probably OK.
That would leave us with the over drive clutch solenoid as a prime suspect.
Again without scan tool operation all we can do is speculate however, getting the system scanned should be a priority after verifying the fluid level is correct.