Try connecting with an IRC client, then when you think your connection has dropped try opening your web browser to a page that your either have not visited before, or one that you haven't visited in a long time. This will ensure that your webbrowser doesn't pull up the website information from the cache stored on your computer.
If you are able to do that, then your internet connection is not dropping.
If you aren't, then call your ISP immediately and tell them, as this means that there's a problem between your modem, and the ISP's server.
Please note that the above is only based on my knowledge, and others may have differing or additional information.
