I brought the Arduino home to see if the stalling behaviour occured on a different network, and the code from earlier (http://arduino.cc/forum/index.php/topic,95531.msg717698.html#msg717698) has already run ~350 requests without a single failure, and that's even without setting the SD pin to HIGH.
All fingers now point at the actual network at my office, which is both great to have isolated as the problem, and infuriating for obvious reasons.
Thanks again for all your help folks, I really appreciate it, and I definitely learned a lot!