I have similar problem with my android phone and Asus router - actually not the same model, but I think it might be related. Anyway.. from the beginning. I'm not a network expert, so sorry for any mistakes (and also for my English, I know it's not perfect...)
I have ASUS RT-AC68U and I've noticed high battery drain on my phone, but actually I didn't relate it to the router on the beginning. I've tried almost anything on my phone trying to prevent wakelocks - frozen/uninstalled dozens of applications etc. but nothing helped. I was fighting with it all the weekend and... nothing. On Monday I went to work and... everything stopped - no strange wakelocks, no battery drainage. Simple conclusion - something with my router settings...
I found that thread and tried the solution with another access point for the android device. I have my old WRT-54GL - I've set it up only as a simple router, within the same subnet as the primary router and it didn't actually helped. I've disconnected WRT from the ASUS, trying to figure out if it's still something from the ASUS router, or maybe because of the noise in the neighborhood. With the android device connected only to linksys everything was fine, so I thought that it might be something sending out by ASUS router to all subnet. I was going to set up linksys as a secondary router with different subnet but I've tried other solution.
ASUS has the ability to create guest wifi networks. I've tried to set it up with the restriction not to access intranet and... now almost no wakelocks on android. When I switch the restriction to allow intranet access, the wakelocks returns, so there must be something sending by the router, maybe to entire subnet, but I don't know how to figure it out.
I was trying tcpdump on the router itself, but I don't see anything strange sending out. I was thinking about ARP requests, which are very often when ASUS'es AiCloud is turned on, but even with it turned off the same things happen, so I'm out of ideas now.
I'd be grateful for any advice, maybe there is some simple explanation of that...