The mechanic initially concluded it was the fuel pump and/or fuel pressure regulator, and replaced both. The paperwork I have says he checked the primary and secondary ingition system, checked the injector pulse, checked CO and HC levels, removed and inspected the fuel pump and mail relays, and checked speed and reference sensor signals.

Later on, he adjusted the throttle, which seemed to help, but the fix didn't last long, and he couldn't find anything wrong with the throttle on subsequent visits. One problem with this is that our mechanic almost never encounters the problem in person. The car fails to start, is towed to the mechanic, and starts fine for him while he works on it for a week and starts it with all kinds of monitoring equipment attached, then when we get the car back the starting degrades slowly until it fails to start, it towed to the mechanic, and the process repeats all over again.