Hey guys,
I spent a lot of time working on this tonight, as I've had similar issues since I got my iPhone 6 in March, and it's been beyond frustrating and no solutions in multiple threads have worked. I *believe* I have this figured out, as I just watched an hour-long stream without wiFi dropping (which never happens), so hopefully this applies to others.
I have a dual band router (2.4 GHz and 5 GHz), with both using the same Name and Password, so devices latch on to either one (how it decides, I don't know). My router is the G1100 through Verizon Fios. I don't know how I got headed down this path but after hours of attempting things I decided to see if I could block my iPhone from having access to the 5 GHz band.
The router login is myfiosgateway.com and the username/password were on my router. In Wireless MAC Authentication I had to check the box that said "Enable Access List" in the 5 GHz Wireless column and then added the iPhone's MAC address to the "Deny devices listed below" list, and hit Apply to save the changes.
Since my iPhone could now only connect to the 2.4 GHz band I turned off Wireless QoS (WMM) for the 2.4 GHz. Whether the two are related (for example, both have to be done, just the first has to be done, or just the second has to be done), I'm not sure, but my phone hasn't lost its WiFi signal since. Granted, to this point we're only talking about a few hours since I made the changes, but typically it'd drop every 10-15 minutes or so and take another few minutes to get it back.