Greg Hyra claims that at least some of the reported connection problems with the modems in PowerBook 3400s are due to the high internal temperature of the 3400 after it has been on for awhile. He writes that when his temperature control strip indicated that the temperature was 98 degrees (which was shortly after starting up), the modem worked. After awhile, the temperature moved up to 106 degrees. The modem then would not reconnect. "The only way it would work again was to put the machine to sleep and let the thermally-challenged modem cool off. This has proven to be absolutely reproducible."
I still find that changing my TCP/IP configuration to a different configuration - and then back again to the original one - usually gets things working again.
Update: Roger Raw claims that his 3400 gets as hot as 119 degrees, and he has never had a modem problem.