iPhone 6s plus wifi disconnect after locking

It’s actually quite simple. WMM APSD (Automatic Power Save Delivery) is a power saving feature featured on some wireless routers. It’s an option that allows the wireless chipset in smaller devices or mobile devices to turn on and off as needed. In theory it should improve battery life seing as your not running two radios. Yes it is true that WiFi saves more power than cellular, but that’s only when data is being transferred (downloading a large file, streaming video etc.) When your iPhone goes into sleep mode large amounts of data (usually) are not being transferred (think of just push notifications mainly) so WiFi turns off and cellular radio kicks in.
If you don’t want your iPhone to keep disconnecting while in sleep mode, go into your router and look for WMM APSD or something similar to power save mode under wireless settings and disable it. Should fix all your problems. ASUS routers tends to come with the option enabled. Also take a look into beamforming. This can sometimes knock off iphones. You may want try disabling those options as well.
Also, Android actually has an option to turn this on and off. I’ve owned every single Nexus, and I do recall under advanced WiFi options there is a (Stay connected to WiFi Always) option that you can change.