I am assuming that you must be using one of the Windows operating systems. Windows OS are infamous for frequent crashes and other issues. Updating Windows can actually make some applications to stop working. So my biased opinion is that this is likely a Windows issue. Try system restore to see if it works.
I have been using Firefox on my Linux operating systems to access AOL webmail for a very long time with no problem. My Firefox web browser came pre-installed on my Ubuntu and Xandros desktops, and I periodically updated them. I further assume that you already have upgraded, updated, reinstalled, and deleted your cache, so I have nothing more to add.
You can bypass your problem by using Linux instead of Windows. Xandros OS will dual-boot with Windows on the same harddrive, and works well with both aol dial-up and broadband. So this is the system that I would recommend.