When faced with a Blackberry whose Hotspot keeps going off on its own, consider this fix:
* Go to Manage Connections and turn on Mobile Hotspot (WI-FI will automatically come on)
* Go back to Home screen > Options
* Select Networks and Connections
* Select Mobile Hotspot Connections
* Untick 'Don't allow any more devices to connect'
* Tick 'Allow connected devices to exchange data with each other'
* Set 'Auto shutoff timer' to a higher value or never