Disclaimer: i don't do much with the stock firmware on these devices and have never used the features I'm referring to.
That said I have a plausible idea of what could be going on.
It sounds like you're using the power saving/sleep features of the device. My understanding of how this works is that at a certain time (or when no one is connected) the device goes into a low power mode and waits for a signal to wake up (WOL packet or similar), I believe these are handled by NasNavigator (or whatever the Buffalo tool for this model is). I'm guessing the special packets used here (UDP broadcast I assume) aren't going through your VPN tunnel and as such aren't reaching the device.
The easiest fix would be to just disable power saving/sleep on the device.
It does seem possible for WOL packets to go through a vpn:
https://serverfault.com/questions/784814/is-it-possible-to-wol-via-openvpnIt might be NasNavigator is just failing to discover it, presumably because it's discovery packets are being blocked rather than the WOL packets. In that case you might have better luck with a generic WOL tool.