The transmission doesn't feel right and selector lights are flashing.

After an extended drive, the gear selector lights flicker and then go out, the transmission stops performing correctly. They pulled over and turned off the engine and were unable to start the car until it cooled down. After restart, it would go for a little longer before happening again. Can take at least an hour before it faults the 1st time. The problem has been present for about 2 weeks and is not getting worse.