You say you can "fix" the problem by unplugging the coaxial cable from the modem and then plugging it back in. Have you tried simply shutting off the modem and rebooting it? What does that do?
I have RoadRunner and I've had similar experiences. First, it was on my end as my OLD (as in older than yours) router bit the dust. Othert times it was RoadRunner's modems and a couple of times it was their lines and switches on the signal's way to me and a several more times I simply needed to reset the TCP/IP stack in my Windows operating system. (You don't state what OS you are using. e.g.: Windows XP, Vista or 7, Mac or Linux.) So, as you can see, a LOT of different things can cause Internet connectivity problems.
Since it seems as if you may have yours narrowed down to that modem, if I were you, I would start with making Comcast replace that modem. That may take several ...or more than several calls..., some arguing and even threatening to take your business elsewhere, but GET that replacement! Then you will be able to come to know if it's your router or not or what, if any, problem still exists. If you still have a problem, then you can test things by running for just a day without that router to see how things act. If your problems vanish, then the answer is obvious. If replacing the modem and [either] running without the router and/or placing
it doesn't do the trick, then the problem is either somewhere out in the field between
the modem and
Comcasts main switches -OR- you have a problem with how your OS is making the connection. IF you are still using XP AND you think that it's the OS that is the problem then you can get a utility called
TCP/IP Repair from here in CNet. Otherwise, you can do searches to find out how to reset Windows Vista, 7 or 8.
NOTE: When you run minus that router, DO make sure that you are running a GOOD third party firewall such as Comodo instead of the one in Windows (if yours is a Windows system) and make double-sure that your anti-virus is functional and it's definitions updated. DO be very careful of where you go on the internet (don't click on any links unless you are sure they are safe. I.E.: a lot of links in Facebook are NOT safe. Use WOT to help you with that.) Do not download anything at all including e-mail. This will help keep out any nasties that may be lurking. If you have internet based e-mail, then there is that much less to worry about, but still do not download anything at all to the computer. By doing these things you will be able to check to see if it is, in deed, the router causing the problem and do it in a more protected way. Once you get the hardware issues settled you can still run Comodo along with the firewall in the router for added protection in a more layered approach which is a good thing!