The bug was just fixed recently in version 2.0.3 of the SDK for iOS.
One developer wrote, "The bug is causing a continual energy impact on the device even in standby. What's even more unfortunate is that the app is crashing or being stopped by iOS (after about 5 minutes) which causes the user to see the homescreen when unlocking the device instead of the last app state."
Here were the steps to reproduce the issue; (1) include GSDAppIndexing in the project, (2) call [[GSDAppIndexing sharedInstance] registerApp: *iTunes ID*] in (BOOL)application:(UIApplication *)application (3) didFinishLaunchingWithOptions:(NSDictionary *)launchOptions (4) launch the App (5) lock the device via on/off button.
Google's John Mueller said today, "Thanks for your report! I took it up with the team, and I believe they just released the update that fixes this. Let me know how it goes & good luck with your app!"
The latest version is confirmed to have fixed this issue. So if you have this issue, make sure to upgrade.
Forum discussion at Google Webmaster Help.