Sorry to hear about your issue with teathering with you BlackBerry. In your post information was left out as to what your teathering to, your laptop, computer? What operating system, windows or Mac? and any error messages that might appear on the device.
A suggestion is to check that you have the VZ access manager based on the operating system your using. You could even try rebooting your device to see if resetting it can help keep you connected.
The link for VZ Access manager is: http://support.vzw.com/how_to_use/vzaccess_using_manager-2.html#a02