I have had the same issue as well for weeks. Even since iOS 8 originally was released (i am running 8.0.2 now on my 5S). I have chatted and spoken with Apple reps. They are not even aware of it basically and say it is not something widespread (great for them, not great for the few of us with the issue). My Wi-Fi at home specifically is not disconnecting (at least that I have noticed), but it is lagging by almost 5 seconds slower than it used to (mail, apps, web browsing for example). I was told 5 seconds is not really a big deal (yes, it is!!)...So keep sending Apple feedback (link below - i've already sent about 5 messages) and lets hope 8.1 fixes this issue...I've also run speed tests and I am getting the same speed I used to (and what Verizon offers me) so it's not my router config.
https://www.apple.com/feedback/iphone.html
FYI, I have tried the following to get my Wi-Fi back to normal:
1) Reset network settings
2) Turned off Wi-Fi Networking (Settings>Privacy>Location Services>System Services>Wi-Fi Networking)...read this suggestion on another site.
3) Restored iPhone from backup via iTunes
4) Restored iPhone from scratch via iTunes (as a NEW iPhone, so no reminisce of the old one at all)
5) Reset router and confirmed it was running latest firmware
6) Turning off cellular data is not an option, because you can't send a normal text message then and is taking away a major feature of the phone, so that's not helpful.
P.S. My wife is running an iPhone 6 and while on Wi-Fi is constantly having to close and re-open such things as Mail and a browser to get things to load properly. Not ideal at all. She also lost Wi-Fi connection entirely (for how long, we aren't sure...About a week into our bill cycle she was halfway through her 2GB data plan!)...I reset her network settings and it looks like that solved that issue...for now...
P.P.S. My other devices, such as my Macbook, are working normally connected to Wi-Fi, so it looks isolated to iOS 8.