I'm at a loss here.
I cannot think of a failure that would cause this unless there was a ton of noise along with it, such as a broken driveshaft that became lodged while it was flopping around underneath the center section, but it would be obvious that there was something wrong, like beating against the floor/ground/gas tank/exhaust as the vehicle moved.
It's possible that the rear differential has had an internal failure and a piece of something became lodged between the ring & pinion gears, and a slight movement in the opposite direction (moving the vehicle backward) allowed this foreign object to fall, which allowed forward movement again. But even here, I would expect gear tooth damage and noise/grinding/chattering to be noticeable. Pull the rear differential cover to drain and inspect the R&P and spiders for damage (chipping, sharp edges, missing teeth), and look for chunks of anything laying in the bottom.
In both cases, I'm surprised that the rear half-shafts survived this sudden wheel lock 3 times without the CVs breaking, if they are truely being shock loaded during this event.
'05 3.0L/Auto, AWD, 262k, stock engine and trans