These random power downs and random reboots also occur WITHOUT wi-fi enabled on my O2 Nokia Lumia 1020 64GB device.
Power down happened last night in LTE coverage area. Had been showing photos of poppies around Tower of London and some websurfing. Works device, so configured to receive push emails, last one arrived at 10:37pm. WhatsApp also recently loaded, last picture message 8:11pm.
On leaving pub at 11pm, I pressed power button briefly, to switch screen to off and put device in jacket pocket. Then drove home (soft drinks only). The battery did not alert that it was critically low, yet I could not get device to wake up, once home. Plugged in power adapter and no sign it was charging. Eventually found this article via a tablet device and used power+volume down to bring the device back to life. Battery had not discharged.
Late arrival to WP8 (WM6.1 before that) so took the Nokia black upgrade as soon as device was out the box. Subsequently taken Cyan (no Cortana yet)/WP8.1.
Model: Nokia 909
Carrier: O2
OS: 8.10.12393.890
F/W: 3051.50009.1424.0004
H/W: 4.4.6.2
Radio: 3.2.04059.1
Chip: 8960
Restarts/power downs are random, but NOT daily in my experience. I will report back this latest observation to my coleagues within Network Integration & Test - Devices team and ask that they raise these issues with their point of contact within Nokia/Microsoft. I don't expect instant attention on this issue, since software/hardware development teams rapidly move onto the next shiny new product to prepare for release.