Of the various smartphones I currently own, I find my new Note 3 has the best Wi-Fi connectivity. Even better than my Nexus 7 which is excellent in it's own right.
I might suggest you check your network first. Recently I experienced some random disconnects. After checking all the obvious areas, I called my provider Comcast. They came out and found a problem at the sidewalk where the city had done some work and disturbed the cable. Upon fixing it, my network was back to normal.
That said there's always the possibility it's your phone, yet rather unlikely. I have a very large circle of friends who like us are enthusiasts. Seeing the vast advantages of the new Note 3, eight of us have bought them. Not one of us has experienced any problems or annoyances of consequence.
Hope this helps.