Ok , the issue may be the carrier if the timeout is not caused by the basic function on the phone. Although apple decided to put in some changes to save user data use it may not be possible to avoid this.
The feature called Touch ID on the phone is a security feature APPLE included on the newest phones. Most users seem to hate the change and if you go to the various apple support sites you will see the complaints.
the timeout feature although possibly intended for the basic access to the phone, may have a bug which sees the BBM password and causes the timeout.
I would hope someone can find a solution for you but it does not look good.
Another possible cause, read this link and see if it applies to your situation. BBM for Android, iPhone, and Windows Phone is unable to send or receive messages over a cellular network