Aol keeps disconnecting.

iMap with Mavericks not functioning properly. AOL says no problem. Apple says no problem. There is a problem and it is with Mavericks. I have several computers. Two have been upgraded to 10.9.1 and others still in 10.8. The 10.8 computers still function normally. Both Mac Minis are having problems since upgrade to 10.9. Both are on different networks and both have been through the mill with reinstalling etc. I spent hours with apple support until they screwed my computer up so badly I had to do a full reinstall. How can we make apple listen. If I go though a browser to imap mail, I have no problem. Only when I use apple mail does the problem exist. Sometimes it make me just force quit mail and restart to get it to connect again. Connection Doctor say nothing is wrong.

After being on AOL since inception, I choose not to change which would require me to change all my email addresses. Has anyone found any solutions to any of this.