The problem lies in the software installed by HP on the notebooks. In this case it is the HP power management software. It goes wrong when the laptop goes into standby or sleep mode (think of only closing the laptop and not turning it off). The laptop gives a command to the docking station to also go into standby or sleep mode but when you connect the same or another laptop to it the next day, the HP power management software cannot send a signal to the docking station to go out of standby or sleep mode (Windows power management can do this, however, it is apparently not possible to uninstall HP power management software).
When you reinstall the HP laptop with a clean (Not HP) windows without the HP power management software, this problem does not occur. Another solution is to disable standby or sleep mode on mains power so that this is only possible when the laptop is running on battery.
A quick way to get the docking station out of the standby sleep mode is to disconnect the Power Adapters and the USB cable to the laptop from the docking station and reconnect it (This works until the HP laptop sends a command to the docking station to go into standby again.