A couple of things could be going on here, but since you said that it happens when you are doing nothing, I'll start with "fixes" for that.
I'm assuming you are using a PC with 95 or 98...even if you aren't, there's probably a similar setting somewhere. There is a setting called "disconnect if idle for more than XX minutes." From the dial up connection screen when you first log on, select settings, then internet properties, connections, settings, advanced and the setting for disconnect is located there. If that box is check, either uncheck it or set the time to a much larger interval. Your operating system may be a little different, but look around for the disconnect setting.
It could also be your ISP. If it is and there is no way around it through them, there are programs that keep the connection alive. I know ZDNet has at least one. Basically, the program sends a signal to your ISP periodically to make it appear that you are being active. Some ISP's can figure out if you are doing this and disconnect you anyway. Of course, someone has written a program that will make it harder for the ISP to figure out if you are doing this.
And as a last resort, you could always type your answers in notepad and then cut and paste them into the web page or whatever.