Steps to reproduce:
1. Open attached project ("892103 repro project.zip")
2. Build to iOS
3. Deploy to phone
4. Disconnect phone from computer
5. Open the deployed app
6. Press home button (to send the app to the background)
7. Wait for a few minutes (so the screen turns off)
8. Open the app to the foreground

Result: "Unity" timer count is smaller than "System" by the amount phone spent with screen turned off

Reproduced with: Unity 5.5.1p4, 5.5.2p2, 5.6.0f2, 2017.1.0a3
Reproduced on: iPad Mini 2 (iOS 9.2.1). Sony Xperia Z3 (Android 5.1.1)

Notes:
* Documents state: realtimeSinceStartup returns the time since startup, not affected by Time.timeScale. realtimeSinceStartup also keeps increasing while the player is paused (in the background).
* Issue does not reproduce if iOS device stays connected to Xcode
* Just leaving the app in background doesn't impair realtimeSinceStartup ticking, it happens after the screen times out.