@rzeczyspisane when you mentioned you were using a dongle that brought back memories (nightmares actually) of the years I spent using a wired USB headset to attend meetings in WebEx, etc.
There was a common hw bug commonly known as the “longer than 1 hour meeting USB issue”. A lot of us came to the conclusion that some USB controller / bridge chip was overheating when in constant use for more than an hour.
The workaround was to unplug from the USB port, wait 10 secs or so (presumably to allow the chip to cool a little and the firmware to detect the new cooled state) and then plug it back in.
I hope that is not the case for your sake, but you might try to unplug your USB dongle, wait some # secs and plug it back in. If you are not able to reconnect then what I am describing might not be related to the problem.
If that does work, then I am afraid the long term solution will be to eliminate the use of the dongle - for example, by using a dedicated bluetooth expansion card on the PCI bus instead.
Hopefully others will have a better answer for you. But I thought I would share my experience from the past …