I was having problems with my wife's iBook modem. It would only connect about 1 time in 3, and would often drop connections when you got it connected.
Someone gave me the useful tip to try the Apple Internal Modem v.34 script instead of the v.90 script. Apparently, the v.90 standard often will try to push the modem speed faster than the line is sometimes capable of handling. If you're having trouble connecting or staying connected, give it a try.
Since switching to v.34, we've had a successful connection on the first try, every time, and have had no dropped connections.
The modem may report a slightly slower speed with v.34, but my understanding is that v.90 averages a lower speed than it actually reports, so you're not really losing much.
This tip isn't limited to the iBook...I got the idea from a Windows user, so it should work with any modem on any computer.