We have been seeing (and continue to see) a large number of users reporting issues of device updates - both over-the-air (OTA) and via iTunes. In most reported cases, the device or iTunes appears unable to contact Apple’s update servers. Whilst it is reported that Apple are aware of the issue, no official acknowledgement (or denial) has been widely communicated through expected channels.
I suggest that it may be worthwhile to manually over-ride the automatic DNS settings on your device - and instead manually select one of the following recursive DNS providers - restart your device, then retry the update.
You can change your DNS settings here:
Settings > WiFi > [Your Network] - touch the “i” icon, then select Configure DNS > Manual and add/replace the existing entries with either of these Recursive DNS providers - both of which are trusted and highly reliable.
Quad9
Primary 9.9.9.9
Secondary 149.112.112.112
OpenDNS
Primary 208.67.222.222
Secondary 208.67.220.220
If the issue you are experiencing is occurring because of bad DNS, this change should be successful in resolving the problem.