I had the same problem. After hours on the phone with tech support (DirecTV and Time Warner) and restarting this, that and the other thing, re-entering IP addresses, etc it was finally resolved within minutes by Time Warner. In my case, the router is owned by Time Warner and they won't even tell me the password - so I am totally dependent on Time Warner to make it right. And their first line technical support technicians don't really have the expertise to do this, and worse, don't know they don't have the expertise to do this so send you down blind alleys and dead ends and waste your time and tell you its fixed when it isn't.
I needed to be very persistent and get to a "level 3" support technician at Time Warner. She "adjusted some settings" on the router and now, no dropped connections. So, in summary, in my case, the router (a motorola surfboard) settings needed to be adjusted by someone who has a depth of understanding that the first line technical support techs don't have.
I should note, I was also getting dropped connections on my other wifi devices. However, this was barely noticeable because the other devices will automatically reconnect within 10 or 15 seconds. For some reason, the Genie won't automatically reconnect until/unless you do a reset.