Something happened and now it works. I did the following two things - I uninstalled the Dell WiFi and Bluetooth drivers and went back to the Microsoft ones. I also updated the display driver, but I guess this has nothing to do with the Bluetooth. I wander why would the first thing do something about it since I was using the Bluesoleil Bluetooth driver. Maybe it was something to do with the WiFi driver. After all, the WiFi and Bluetooth are physically the same device.
Anyways, now I can go back to my usual way of just hibernating my laptop instead of rebooting it.