hmm, im suspecting the technology is the same when 56k was first being "consumerized" that the connection is totally dependent on software. what connection is the modems interface? is it USB? check for conflicts with the USB port.
[edit] read post properly and saw Mac-like words.... good chance its USB and totally software controlled.
when you have a software 56k modem, after 20 minutes of UT the sae happens what you described, thats when the modem is becoming too much for the CPU to keep it running. i think the same might be happening to your connection, but im not totally sure because wireless connections here (even tho designed for my area... thank you BT) are never gonna be deployed. [/edit]
/me runs away from mac-like words!