Update: I finally got around to calling my ISP today and told them about my problem. They said they were detecting my modem was a little off in its frequency and would send a guy over to take a look. My complements to Grande communications, the guy already came the very same day I made the call. He replaced my modem which was about 8 years old.

So instead of disconnecting every hour at a quarter past, my connection is now dropping every hour at a quarter till. I guess that's some kind of progress. I'll give them another call tomorrow.