Why does my aircraft appear to fall to the ground when I cross a sim border?

This is one of the many and varied symptoms of "lag", and there's little that we users can do about it.
When a vehicle crosses a border, the first sim has to release all of the objects data and script states to the second sim.
This transfer procedure usually takes less than a second, but in some cases can be several seconds.
It's not uncommon being disconnected from both sims just by crossing a border, with or without a vehicle.
During the handoff, the SL attempts to predict the path of your vehicle ballistically, so you will appear to fall.
If you have problems with unusual delays or disconnections while crossing a border, contact SL support: support@secondlife.com.