I have a Pixel 9 Pro. I believe this has been happening for the entire time I've had this phone (since early September), but I am not sure about that. If I turn Bluetooth on again with the notification settings toggle, it will stay on for a while. I'm not sure how long before it turns itself off again. I usually don't notice it has turned off until I get a phone call while driving - I have to dig the phone out of my bag and turn Bluetooth back on.
Before the Pixel 9 I had a Pixel 7 and never had this issue.