I experienced this few times when I was on dial up. It was random and not persistant. That is, change it back and it would remain as it should for a long time. I didn't really find anything that was causing it.
The only thing I recall was making sure the connection details in avast where set correctly. I know it's not supposed to make a difference but read on...
After I switched to high speed, on occasion the connection setting would change from never dial a connection to Dial whenever a network connection is not present and the connection box would be on the screen. The setting in avast would also either be changed or none selected.
This leads me to believe that in win98 the 2 are related. When windows sees something trying to access the internet it will popup the dialup box. In this case, avast.
Now that I've justified the suggestion I'm going to make
Check the setting in avast
right click the "a" icon
select Program settings
click Update(connection)
Make sure it's set to dialup.
Like I said, the 2 aren't supposed to be related, but maybe win98 sees something we don't.
I never did determine what caused the changes or have any real proof, just my experience.
I think was using