2004 Corolla intermittent reverse problem

My girlfriend's 2004 Corolla has been having intermittent problems going in
reverse gear.  For the past week, it's happened 3 times.  Once, she was going to
work in the morning (cold engine) and put the car in reverse out of the driveway.  
The car didn't make the usual engine sound of switching gears.  It was like it was
still in park.  Pressing the gas didn't make it go in reverse.  She tried drive and
drive was working, but putting it back in reverse didn't do anything.  The engine
would just rev.

Another time she was making a U turn (so the engine is warmed by now), and it
happened again.  She couldn't go in reverse, but drive was still working.

She had the transmission fluid drained and refilled.  It happened again yesterday.

Any ideas on what might cause this?  The mechanic she went to had no idea.  He
couldn't find anything obvious.