You don't have to worry about crashes. Firstly, you can always download a copy of Little Reader and your license key from your Account Management (Software) tab (see where it says "Account" on the top right of this page). You can also uninstall and reinstall on the same computer, and it will remember that you have a license key. If you want to move your LR to another computer, just let us know when you do that, and we'll switch your license for you to the new computer.
I have moved your download problem here:
http://forum.brillkids.com/little-reader-bug-reports/can't-download-playlist/