This is an older post with many ideas for resolving this issue and here's how I resolved mine. I have a Galaxy Note 3 and had the same issue for nearly 6 months until I finally figured out what was going on. I'm sharing here in case others have a similar set of circumstances.
1. I have a router (Fios) that supports dual band (2.4 & 5gHz) WiFi frequencies. When I set up the router, I thought I would make it easy for everyone wanting to connect to my home network and named the SSID the same for both radios (in my case, "MyWiFi"). This seems to work for most phones because many older phones don't support the 5gHz band. So, when those phones connect, they are connecting to the MyWiFi 2.4gHz frequency and they stay connected because there are no other options their phones support.
2. My Galaxy Note 3, like many newer phones, supports both band frequencies. Thus, when I set the WiFi setting on my phone to connect to "MyWiFi", it connected to either the MyWiFi 2.4gHz or 5gHz band, depending on how far away I was from my router. Although the 5gHz band provides a more stable connection and is generally preferred, it also has less range than the 2.4gHz band. Thus, depending on whatever interference I was experiencing while walking around the house, my phone would many times drop one band in favor of the other (remember, in my case, both SSIDs were called "MyWiFi"). So, it always appeared that the WiFi connection would drop, connect to 3G/4G, and then later reconnect when in fact one radio frequency was being dropped in favor of a better signal (both of the same SSID).
3. SOLUTION - I simply changed the SSIDs on the two bands of my wireless router to:
(1) MyWiFi-2.4gHz and
(2) MyWiFi-5gHz
This has resolved my WiFi disconnects and allows older phones to still connect (older phones will only see "MyWiFi-2.4gHz"). Dual band phones will see both WiFi frequencies and should pick "MyWiFi-5gHz" in this example (unless the house is huge, the 2.4gHz connection could actually work better).
CONCLUSION - If anyone has:
(1) a dual-band wireless router, and
(2) happened to setup the SSID on both radios using the same name (like I did), and
(3) your phone is a dual band phone like many of the newer Galaxy (and iPhone) phones,
the solution above may resolve your problem. It certainly fixed mine.