Update for me.
Since I changed my mail-checking intervals from 5 to 10 minutes, there was vast improvement in this problem. For quite a while it virtually disappeared, it was just like the good old days when it pretty much never happened.
A couple of days this past week the problem came back with a vengeance, just as bad as when it was peaking when I started this thread. But I went onto google and found a lot of internet chatter hinting that it appeared to be a network-wide aol issue at their end, since many people nationwide were having the same problems. So it sounds like I would've been getting the pop-ups regardless.
It seems like for about the past week, aol themselves have been having significant problems with their email systems based on internet feedback out there from other customers, therefore it's making this problem much more difficult to troubleshoot since now you don't know exactly what the root cause of the pop-ups is until aol gets their end of it solved. I can definitely tell you that raising the time intervals for send/receive from 5 to 10 minutes did seem to go a very long way towards solving the problems with the pop-ups. Even though I'm still getting them, here and there, I think the ones I have been getting lately have been due to problems at aol's end more so than mine, based on other aol user's feedback. I'm hopeful that I might be at the end of the tunnel regarding this issue but thanks to what's going on at thier end (aol) I can't say for certain yet. I'll keep you posted.