Hi there. My name is*****'m sorry that you're having this problem. It would be my pleasure to assist you. Does the book partially download? If it doesn't download at all, you may need to log in to your Amazon account (https://www.amazon.com/gp/css/homepage.html/ref=nav_youraccount_btn)and click on Manage Payment Options under Amazon Wallet. Check your payment settings and update if necessary.
Have you had your Asus TF101 for very long? Sometimes, this happens when your device is almost full. If this is the case, you should be able to delete a few books form your Kindle and then try again to download it. If you have a lot of books that you'd like to delete, it may be easiest to just delete the Kindle reading app, reinstall, and then re-download just the books that you want. It may be helpful to delete and reinstall the app even if it's not due to your library being full.
There are 3 different methods for deleting an app from your TF101. They are all pretty much the same as far as removal, just which is easiest to execute.Method 1 - From the app drawer, long press the app. It will go to the home screen to place it, but if you drag to the top of the screen there is a "Remove" option (unless it is a pre-installed app). Drop it on the Remove and it will be uninstalled.Method 2 - Go to Settings - Apps - All - Find your App - UninstallMethod 3 - Open the Market, find the app, Uninstall.
Please give these troubleshooting tips a try and let me know how it works for you. If this solves the problem, would you mind taking a moment to rate my service? You can give your rating by selecting the stars located on the top right of the question page. I'd really appreciate it! Without a positive rating I am not credited for my answer. If this doesn't solve the problem be sure to let me know so we can continue troubleshooting.