Nick, I am back, sorry for the delay. I am going to give you a long explanation so bear with me, I hope it helps.
I know your comment about "going mad" was in jest but regardless, let me assure you that no meds are needed, there are many having the same problems. I will start with some facts about the state of the issue and then I will offer some suggestions for your specific case.
I have been following this thread since November 2014. In summary, the problems with Wi-Fi occur on a subset of devices as the majority of users are not having issues. However those that are often report serious difficulties. I am lucky - in my own case my 4 iOS devices connect ok but have difficulties with slow download speeds when Bluetooth is turned on. They function at full ISP speeds with BT off. However my MacBookPro as well as my two Dell PCs work perfectly well with the same router (Cisco) regardless of Bluetooth settings. I have posted on this thread many times and as a result I and others who did the same received calls from AppleCare. Apple collected various logs from my iOS devices and took extensive information regarding my Wi-Fi configuration. The calls - 2 of them - lasted over one hour each. Others have reported the same. So Apple is aware of the issue and is working on it.
Apple used to use a networking routine called mDNSResponder in iOS 7 and in OS X Mavericks. With the advent of iOS 8 and Yosemite they changed to a new routine called DiscoveryD which has been quite problematic for many and its issues have been extensively reported on the web. However when Yosemite 10.10.4 came out, users noticed that Apple had switched back to mDNSResponder, easy to test with Activity Monitor. In Apple’s 10.10.4 release notes they stated “improvements to Wi-FI”. While there will always be people posting about Wi-Fi issues (on any iOS, Androids, Macs or PCs) the general consensus from technical publications and affected users is that reverting back to mDNSResponder has significantly reduced the problems encountered with the previous networking routine (I rather not post links to non-Apple sites here). According to Apple, iOS 9 will be released in the fall and hopefully there will be improvements there as well, that is all I can say at this time.
There have been some so-called “fixes” reported here and there but most of those “fixes” have not proven successful in the long run (see my post on page 206 about the middle of the page, 7/29/15, don’t know what time zone you are at, so the time stamp would not help).
In the mean time I have some questions and suggestions for you.
1. Do you have other wifi devices at home, PCs, Macs, other iOS, Androids? Do they work ok or not?
2. Are you using the 2.4 or 5 GHz band on your Asus and have you tried connecting your phone to the 5 band? Any change?
3. Do you have Bluetooth and AirDrop turned on your iPhone 6? If so turn them off (BT to off will suffice) and test again?
4. Do you have Google’s DNS on your phone? Slight chance it could help.
5. Do you have the OOKLA Speed Test App on your phone? If not, install it from the App Store (free, but assuming you can get connected and you may not, grrrrr) and compare what you get on your phone with what you get on your Mac/PC (no app needed there, just go to speedtest.net). Make sure no other device is using wifi while you are running the test (best to have them all on sleep). If your phone is not able to connect this is moot.
6. On your PC/Mac do you get anywhere close to the 80 Mbps you are paying for?
7. Have you tested your phone at a coffee shop’s wifi or the like? Even if it works ok there, that is no guarantee that your phone or iOS is ok. I can explain later if you like, but to save me the trouble, test it at Starbucks first and see, or alternatively at a neighbor’s or friend’s wifi.
8. You said that you updated the router software, how old is the router? Moot if wifi certified and all other devices work ok but curious anyway.
9. You said that you did a full restore. Did you do what is on this link:
Use iTunes to restore your iPhone, iPad, or iPod to factory settings - Apple Support
and if so did you restore from a backup? If you did that and you have a corrupted App or system setting, you would be restoring the corruption as well. I can help with this once I know the answers above.
10. Some have reported success by replacing their router with an Apple Airport Express but hardly a solution for all with rather new, major brand, networking equipment (Asus should be fine) and also in good up-to-date operating condition. Apple to Apple does seem to add stability.
I will comment again once I know the answers above. Also fyi there are several threads on this forum regarding iOS 8 Wi-Fi issues. While this one is the largest and oldest, if interested check this one out. Wi-Fi not working on iOS 8.4
If none of the ideas above help, just hang in there until iOS 9 is out in the fall. Trust me… ✅
elcpu