I use XP, so I can't be too specific about ME, but check the 'Properties' settings for your dial-up connection (Programs - Accessories - Dial Up Networking) double-click the connection icon and select properties or settings. Or right-click the connection icon and select properties (as I said, can't be too specific). Somewhere there is a setting which says "Disconnect if idle after xx minutes" (the xx value can be set by you)
That means, for example, if you load a web page and sit looking at it for more than 'xx' minutes, the PC/Modem will think it's an idle connection so it will disconnect you.