Did you check your modem setting like I showed in the image to set it to Never disconnect?

I've never used AOL so I don't know what options they give & what rules they play by. Some dial up providers will disconnect you if they detect you haven't used the browser to go anywhere or other net search after a certain amount of time.

Dial up is 56 kbps which means you only have a maximum speed of 7 to 8 KB/s. There apparently are super speed dial up services now but I know little about them & I think you'd need to pay more for them. If you want faster speeds then you should be looking at broadband or cable connection. Those people who get 27 TO 40 KBS are using either broadband/adsl or cable. The other advantage of these over dial up is that they leave your phone free to use. If you're using dial up you can't use your phone at the same time. But they cost much more depending on your area.