My wifi connection is rock solid. I just upgraded to an Asus RT-N66U router about a month ago and couldn't be happier. Every room in my house gets a solid 3 wifi bars on all of my iOS devices. I haven't had a single issue with this router, so I highly doubt it has anything whatsoever to do with my router.
However, the Apple tech that I spoke with on the phone did say that the iPhone chooses whichever connection is best and uses that one. I assume this means that if over LTE you were getting 20Mbps download speeds and if your wifi was only getting 1Mbps download speeds, that your iPhone would switch to the LTE even though you have wifi enabled.
Now, if this is true, then how does the iPhone determine the "best" connection? Over my wifi network, I get around 40Mbps up and down. Over LTE, I am around 20Mbps. So as long as I'm not downloading a bunch of stuff from another system, then it should choose wifi. However, if by "best" it takes into consideration other factors such as ping, etc. (I'm no network engineer), then it may indeed choose LTE over wifi.
Anyhow, the Apple tech I spoke with said that she'd talk with her engineers and get back to me tomorrow, Thursday. Any enlightening information given to me, I'll stick in here.