This shouldn't happen. But like many other things that shouldn't happen, they sometimes happen anyway. On the good side, there'a quick remedy for this. But one thing at a time, read and do this first:
Backup the books you currently have in your ReadMe! library. To do this, please follow these steps:
1. Connect your device to a computer
2. Open up iTunes on your computer
3. Click on "Apps" in iTunes
4. Scroll down and select "ReadMe!"
5. On the right hand side you will see a list of all your books in ReadMe!, they will have the file-extension ".epub". Select these files, then drag them to a folder (or your desktop) with the left mouse button.
Please make sure that your books have all been transfered to your computer before you proceed.
Ok, now when that's taken care off you may continue reading here. Basically you just have to uninstall ReadMe! altogether and then install it anew by downloading it again from the AppStore. This WILL delete the books you have in your library, but since you followed the steps mentioned above you have backups that you can transfer back to your ReadMe! library once the reinstall is finished.
To uninstall ReadMe! from your device you simply hold down your finger on the ReadMe! icon until it starts to jiggle and you see a small "x" at the top left of it. Now tap on that small "x" on the ReadMe! icon and then confirm that you want to delete this app.
Then when all of this is done, you just go to the AppStore on your device and download ReadMe! just as you did before. Since you've already purchased ReadMe! before, you will not have to pay anything to download it.
Once it's installed again, you can safely transfer your previously backed up books back to ReadMe! by following the instructions here: How to transfer books to ReadMe!