My theory on this one is as follows.
(1) In any bank of dozens or thousands of modems you'll get one that fails from time to time.
(2) Sometimes instead of going from fully working to fully dead they go through a period of sort-of not-really-working.
(3) If the modem rack is pretty busy then naturally it'll be the neary-dead ones that are available to answer calls ... for the simple reason that they aren't working properly so nobody is using them.
(4) So if you keep re-dialling you'll keep getting the same nearly-dead modem.
Solution: try again an hour or two later, when the traffic pattern will have changed, or the nearly-dead modem will have died completely and won't be attempting to answer the phone any more, or someone will have spotted it and taken it out of service.
Be interesting to hear from any ISP techies as to whether this theory does actually make any sense or not (I've only worked on dial-in systems for a handful of modems at a time).