We have received reports from people who are finding themselves repeatedly logged out of Newsstand apps and other apps after the IOS7 update. According to The Verge, a bug in Apple's new back group update API could be the cause.
You can find more information by following this link: http://www.theverge.com/2013/9/23/4761860/ios-7-bug-snapchat-mailbox-loom-logged-out
In the meantime, you can turn off background refresh by following the instructions below:
- Tap on "Settings" on your device (not within the App)
- Tap on "General" then "Background App Refresh"
From here you will find a list of Apps, switching the toggle to 'off' for the App should resolve the issue.