My Internet Keeps Cutting Out

Hello,

I've been having this problem with my internet recently that I can't seem to solve, and is frustrating me so much. Would love some help.

Basically, my internet is running fine for periods, then all of a sudden it kind of drops. All of a sudden I can no longer open new pages in my browser, it will just say cannot load page, but everything I already have on the internet still works. For example, if I am logged into an online video game like Runescape, that stays connected, and I can keep playing online for hours without it cutting out, but if I log out and try to re-log in it'll say can't connect to servers.
I reset my router, which fixes it all, but then this problem comes back shortly later. I am looking for a permanent fix, because having to get up and reset my router every 10-60 minutes gets really frustrating.

What makes me feel like it's not my computer that is the problem, is the fact that the same thing happens on my Xbox One, which is hardwired into the router (computer is on wifi). It'll be running fine, but then I can no longer do anything that requires internet to do, like check my friend list. But stuff like my downloads keep going even though I can't start new online processes.

Any help would help me out tremendously, thanks.