While I am downloading email, my dialup is disconnected in mid-stream. My provider thinks it is my antivirus program which is AVAST Home. Any suggestions or recommendations? Thanks
avast does not have any dialer not antidialer.
I use it in a dialup and, of course, it’s not avast fault that the line is droped.
I’m a little bit surprised that your provider tried to show you that… :
If you want a connection keep-alive, I think there is some suggestions in ‘Links’ on my signature 
This could be due to large files being downloaded and the connection is timing out, change the Time out settings for your email accounts.
Taking a guess as you don’t give us an email program - For Outlook Express - Tools > Accounts > select account and click Properties > Advanced and change the timeout setting, see image.
I’m not surprised that you ISP is passing the buck.