Is the router resetting itself or is your broadband provider resetting itself?
If your ISP drops your connection, a new router unfortunately won't help, but if you start jotting down times when it happens, your provider *may* be able to investigate if something on their end is the reason for the drops/resets.
And yes, the internet is a huge, enormously complex thing. I've had plenty of times where my ISP had issues and I'd be connected, but get horrible horrible speeds. Tech support would reboot my modem, ask me to plug it directly into the computer, blame my splitter, basically say anything but that the problem could be on their end, and if I'd like they can send a tech out to my location... I knew it was nothing between the pole and my house, so I'd just say f it. Usually it will clear up down the line in time, and it's usually because they fixed something and don't tell you about it. Big ISP's get tech issues/failed hardware just like home users, just they don't often notice as quickly, or report it...