The built-in clock would be constantly powered, just like your PCs clock is. Obviously if you drain your battery all the way the Kindle could forget what time it was, but there's no need to do so on a Restart.
In any case, that's not what's happening here, either. The Kindle still knows what time it is, as can be verified by accessing the Menu. It's just that when it can't access Whispernet after a while, it stops timestamping files when you access them. According to Windows they aren't timestamped back to 1970; they aren't timestamped at all, but that could be just a Windows display issue.
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