kmccune, I won a ISP so I know what you are talking about exactly. They are using more than likely a ISDN-PRI as their call in line. That only has 24 lines. One line is always connected so you actually get 23 lines.
So that means when you dial in and you are the 25th port, you dont get in. Depending how they have their authentication accounting setup. You might bump someone off that has been online for a while, thus when you get bumped off this may be the same senario.
ISDN-PRI's are known to go into LoopBack test by themselves, thus causing the line to go down adn anyone who is on it to get disconnected.
Are you using a Hot Call box of any kind?
This may be your problem as well adn not the ISP.
Cheap ISPs suck, their equipment is all budget stuff and they think by shaving costs in equipment they will save money/ Dont work that way.
Like PecBell, we own our own 5ESS switch, and our own fiber network. We rent nothing from nobody. So we have total control of our lines and network. Most ISP's only dream of this.
Get an ISP that is strong in equipment and not in image.