Internet connection resets multiple times an hour

I have had this issue plague my family for years, and I am beginning to think that I am the problem. Here is a summary of the problem:

My internet connection cuts out randomly. It goes completely dead for all connections (wireless and wired) and behaves almost exactly like it does when the modem is reset. This is happening multiple times an hour, and as non-cable users, this is really destroying our Netflix/Hulu/HBO enjoyment.

We can skip all the basic troubleshooting:

• I am primarily testing hardwired with other wireless devices
• The modem is not on a surge protector
• There is no coax splitter on the cable line
• I do not have cable tv
• I just got a new modem this evening from Cox, same problems. Happened 5 times in the past hour and a half.
• I see a "No Ranging Response received - T3 time-out" error in my modem logs around the time of the drop, but this is not the constant message. I just cleared my logs so I do not have the others handy.

Now here is the frustrating part for me. I had this same issue (albeit not nearly as frequent) when we lived in Nashville just a couple of months back. It was happening for years, but was only a few times a day so it was not nearly as frustrating. I had technicians come out there, modems replaced, etc, and it would always get a little better but eventually go back to "normal" (cutting out regularly).

For the life of me, I swear I am not doing anything strange. We have my desktop hard-wired, with semi-regular downloads of games on Steam, and several nights a week of online gaming. We have a Samsung Smart TV, which we use for Hulu/Netflix/HBO streaming (a few hours a day. We have two smartphones that are used for Facebook and Reddit. Is there anything that I could be doing that is causing this issue?

Are there any other people who are more familiar with this type of issue that can help?

For the record, I have been in software development for nearly a decade, so I tend to understand a lot of technical lingo; hopefully this will help with any discussions that may occur. I will be the first to admit that I don't know jack *** about hardware networking or any sort of networking details besides the basics of how the internet works (or is supposed to in my case).