iPhone 6s keeps dropping wifi
I got my iPhone 6s on launch day. I've been having trouble with the wifi connection since day one. Even before I got through the initial setup it was having trouble with wifi. Since then I've had constant problems with it staying connected when I'm at home. I'll try to send a text from my iPad and it will fail because the iPhone is not connected to the network. I'll look at the phone and It'll say LTE. As soon as I open settings it reconnects to wifi. If I just leave it sitting on the wifi screen I can see it constantly dropping the connection and then reconnecting. Occasionally it wont reconnect, even though I can clearly see my router on the list below and when I click on it it reconnects.
I've done a full reset of the phone and reset the network settings twice. It still has issues. Has anyone else had this problem? Could this be a hardware issue? Or is there some known software problem?
My router is a TP-Link 2.4Ghz 802.11n model that's a few years old. It has the latest firmware and I never have any issues with any other devices connected to it, including my iPad Air.
iPhone 6s, iOS 9.0.2