My mobile broadband plugs into the laptop usb slot and looks like one of those thumb drive things
This seems to be an external USB device from 3rd party manufacturer.
Did you check the manufacture page for some suggestions or possible solutions?
Maybe there are some new driver updates for this device.
As this device is connected to the USB port I would also recommend disabling the power saving for USB ports.
In device manager expand the USB controller section. Here click right on USB root Hubs and go to properties. In Power Management tab remove the mark from option: Allow disable device to safe power. Do this for all USB devices.
Do you have the notebook problems if this USB devices is not connected?