Wifi stays connected but Internet connection drops constantly - Macbook Air 13" Setup:


Computer: Macbook Air 13-inch (early 2014) 1.7 GHz Intel Core i7, 8
GB, running OS X El Capitan. Using DHCP &amp; automatically configuring IPv6
Router/modem: Netgear N300 Wifi cable modem router, Model C3000 
ISP: Time Warner Cable


Problem:

Wifi stays connected, but ceases to have internet access constantly. I can regain internet access by either cycling the wifi on and off from the top bar, or by running "Diagnostics" in the "Assist me" section of the Network System Preferences. 

When I run Diagnostics, the Network Status shows up green for Wifi, but red for wifi settings and everything below that. The actual act of running the diagnostics fixes the problem.

I've tried power cycling the router, the computer, and the cable box, as well as renewing the DHCP lease. It seems to improve the length of time between internet disconnections, but they still happen somewhat often.
What version firmware is present on the net gear?  Does this also occur if you are hardwired in?  Can you disable the N band temporarily to see if that changes anything?