I am on an Intel Mac OS X 10.5, and this issue has come up when I use both Firefox 9.0.1 and Safari 5.0.6.
When I am in Jigsaw, I have noticed that, while clicking and holding down onto a piece to drag it, if I accidentally drag it past the boundaries of the window but bring it back (never letting go, mind you), the piece disappears once I release the mouse. Closing down the window and opening it up again restores the piece, though, so there is no permanent damage (unless you didn't save your puzzle). If you save after the piece has disappeared, the piece does not come back. Shuffle does not bring back the piece either.
I made this thread partly to alert Gaia of this issue, and also to let others know that, if this happens to them, don't save the puzzle. Just open it and close the window. You may lose your work, but better than getting to the end, realizing a piece is missing, and having to restart the puzzle.