Not sure what the proper terminology is for this, but... There are two different appearances for the inbox in the Stack Exchange app. There's the one you can get to by clicking the counter in the top bar:
Clicking this... 
Brings you to this... 
And then there's the other one, which seems to only show up if you tap a notification in the system notification pull-down and the app isn't already running:
Note that there's nothing to it but the inbox - you can't any other part of the app. It's almost as though it's a separate inbox app... An impression that's strengthened when tapping one of the messages pops the splashscreen before finally taking you into the main app. This isn't the bug I'm reporting though; maybe it's intentional, and if nothing else it's really not too annoying...
But what is frustrating is the fact that you can't get back to the "inbox app" if you leave it. Not a big deal, if you're leaving it for the main app since you can always get to the inbox there - but if you're leaving it to jump into a browser (say, because you tapped a chat notification) or answer a phone call, or even just opening up the app switcher (where it does appear, initially)... It disappears without a trace. The "back" button takes you to the desktop, and the app disappears from the "recent apps" list.
Not a big deal when there's only one new message, but pretty annoying when there are several.
