We often hear from the users who were surprised to discover that the PDF documents stored on their iPads/iPhones disappeared after uninstalling Adobe Reader for iOS.
Here's the new document that I just wrote.
How to backup and restore PDF documents on your iPad/iPhone using iTunes
Hopefully, this will help you recover your lost PDF documents.
An alternative is to store all of your PDF documents on cloud storage (e.g. Acrobat.com, iCloud, Dropbox, Google Drive) all the time. Then you will not lose your PDF documents when you uninstall Adobe Reader for iOS. But you may not always have Internet access to read/write documents from/to the cloud storage.
Please let us know if you have any feedback or suggestions on the topics for other help documents/tutorials.