Things got crossed there. Have you tried the latest firmware for your router?
If not then update it and perform a factory reset and re-enter your settings again. They looked ok. Just to reiterate:
Auto Configuration Setting Stateless
Connect to DNS Server automatically Enable
Enable Router Advertisement Enable
Odd behaviour, some Asus models seem fine. Are you using the same Asus router? The RT-AC3200.
Might be another firmware bug.
Clutching at straws here, you might want to try different DNS servers rather than auto. Assuming you don't do that already.
Sorry for the confusion guys, took the data from the wrong post. Oops.
The issue is odd. BT apparently got the intermittent IPv6 problem resolved. So it shouldn't be related. This makes it more likely the firmware is still buggy.
A thought, is there anything that looks vaguely like 'Automatically negotiate a global address' in the Internet IPv6 settings?
As nothing tried seems to help it looks like waiting for a firmware update is all that's left. Unless you feel like returning it and swapping for a different model that is known to work with IPv6.
For example the one @Jonkarra is using. Just a thought.