One of the biggest gripes from people who tried BBM during the original failed launch was that you had to live with a persistent notification in your status bar. BlackBerry responded with a setting in the beta version — which found its way into today's actual launch — that allows you to turn off that nagging notification in your status bar.
But you probably want to leave it alone — if you actually want to get messages, that is.
Google, in its effort to fight apps that suck down battery or stay alive to watch you without you knowing, now requires any application that wants to stay alive at all times to place a persistent icon in your notifications. When this is done, and that icon is showing, that particular app won't get closed, no matter how much RAM active applications are using. It's treated as a foreground application, even though not it's actually open on your screen.
When memory does drop below a certain threshold on our Androids (that level is determined by the people who built your particular version of the OS), apps not being actively used start to get shut down. If you've disabled the persistent notification in BBM and forced it to act like a normal app instead of one that's always running, it can and will get closed when memory is needed elsewhere.
Because BBM doesn't use Google Cloud Messaging (GCM), you won't get chat notifications when it's not awake and listening. When there is enough free RAM for it to restart (it tries to run all the time per the app's permissions) you'll get the notifications then, after it restarts.
There's no real way to fix this, because BlackBerry isn't going to ever use GCM and Android is never going to allow apps to run willy-nilly without the user knowing.
So if you want to use BBM, just leave that nagging notification alone.