Lost internet connections

I had a continual run of problems with my internet connection for about a month at the beginning of this year. The Local Area Connection icon said the computer was connected, but not a thing was happening. I ran numerous virus checkers to make sure I hadn't been unwittingly invaded, and tried unplugging and replugging the router and the wireless modem (which resets them), but none of this helped. After consulting with Those Who Know More Than Me in the IT firm next door, I concluded the problem was at the service provider's end. Possibilities include overloading of the circuits in our area, etc. Suddenly the problems vanished, and things have been fine for the past three weeks, which almost certainly indicates the problem was not on our computers.
From talking around, it seems the problem is fairly common. For another take on what can be going on, see this response at PC World to a query by one Margie Miller, who keeps losing her internet connection and asks, is it the router, the modem, her PC, or something else?