Unfortunately I'm facing the same issues here.
I searched around and the "Bluetooth Problem" affects other phones as well with similar symptoms, so it's most likely the software that's giving problems. There were varying success with setting the visibility to never timeout. I tried that and it worked for a short while, sadly now Bluetooth is MIA again...
The problem with this problem is that it's hard to nail down the root cause or reproduce consistently, so workable solutions are hard to find. There's an app
on the Play store that claims to fix Bluetooth problems but it requires rooting, so I couldn't try it out.
Hmms looks like updating to 4.2.2 doesn't solve the problem for some of you... less rush for me to upgrade then.
Yeah, I also tried one factory reset on the phone, putting it in/out of flight mode, turning the phone on/off, and even toggling Bluetooth quickly trying to "jump-start" the underlying processes. The only change I noticed was when I was attempting the last option, I could briefly see the phone trying to disconnect from my car's Bluetooth, so it looked like something might have worked. For now, I'm just trying to live with the inconvenience every weekend when I drive.