Bohan, just glancing through the cameras I have here, or have easy remote access to...
My IQ511 and IQ753 do not have any auto-reboot function that I can see, although they do support some significant scripting ability and it may be possible to "add" such a feature that way.
The Dahua cameras on my bench do have an auto-reboot function automatically enabled to go at 2:00am Tuesday... seems to me I have noticed this before but have never bothered changing it. Once a week in the wee hours doesn't seem like a significant issue.
The Axis P3384s do not appear to have an automatic reboot feature.
I can find no automatic reboot in older HIKvision models... don't have a newer one handy to see if they support it.
Looking at a Vivotek IP8162, there's no auto-reboot there either, unless it's well-hidden.
And finally, an Arecont... nope, nothing there either (not surprised there, though - they're very limited in administration).
You're right though, it's something I've never actually looked for, as there are far too many other things that require tweaking just in a camera's admin interface, nevermind in the NVR itself, or the physical installation. As I say, now that I look at it, I believe I have noticed it in the Dahua, but never paid attention to it.
As for whether the camera keeps working when the OS crashes... well, I suppose it depends on the actual cause of the crash, and just WHERE it happens. At some point the interface OS has to interact with the video processor. A bug in firmware code for the encoding and/or compression itself could cause a crash at that level. Of the camera failures I've seen, few have been simply an inability to get into the admin interface while the camera keeps sending video to the NVR.
Then again, maybe the interface crashes a lot and nobody ever notices, because nobody tries to access it except to see why a camera is no longer showing up in the VMS?