Update. I've been able to work around the issue. I didn't think about it until last night, but here is my current workaround (using 9.3.1). I don't have 10 yet, so the new tool doesn't help.
The model will run through 30 iterations before it stops working. When it stops working, as I stated before, I am unable to run even the Extract Values to Points tool manually. At this point, if I close arcmap and reopen it, the model will run to the same point, or I can use the tool manually again. So, this is what I have done: I run the model until it crashes (all my intermediate data is left behind), then I close and reopen my project and the model, highlight the command in the model where the error occurred, and then click "RUN" instead of "RUN ENTIRE MODEL". This effectively continues the model where it bombed out, working just fine until the model closes without any further errors.
So, I run the model in 2 parts, with a full shutdown of arcmap in the middle. It's ugly, but it works. Thanks for the replies, I checked all the stuff mentioned, and with the new version of arc available and the new tool, I don't think I'll spend the time to submit the error.