It was specifically the call-waiting beeps that interrupted the modem connection. I recall my 300 baud modem tolerating it, but 12/2400 (and higher) could not recover from the interruption.

You could set how long the modems would wait for reconnect. We had a service that offered free phone calls with 15 seconds interruption for ads now and then. Worked fine for free bbs time if you knew how to set it :)