Out of curiosity, why do you want the countdown to stop? Are you having that much trouble making up your mind about whether or not to rebuild? I'm pretty much unable to think of some circumstance in which I would want SW to sit there waiting longer than 10 seconds for my input on that question.
I've got your circumstance right here:
I was filing an ER because the option buttons should say "Yes" and "No." Not "Rebuild" and "Don't rebuild," and I wanted it to stay up so that I could refer to it while submitting the ER.
The question "Do you want to rebuild?" is asking for a yes/no answer. Consistently, your answering options should be yes/no, with hot-keys of Y & N, not R & N.
So there you have it. :-)
I guess that in regular practice it's ok. I just generally expect automatic dialogs like that to stop counting once I give it an action. Which is how every other one I've seen behaves.
The timer was added to this dialog in 2008 to address the problem where a user would begin a long rebuild and then go do something else (such as getting the figurative cup of coffee), only to return and find that SolidWorks had been sitting there the whole time with a dialog box open.
While there is no way to stop the countdown per se, you'll get the same effect by simply pressing the "No" button. This aborts any rebuild and closes the dialog -- you can press the Rebuild button at any time after that if you want the assembly rebuilt.
It is of course theoretically possible that a user might need more than 10 seconds to read the message and make their decision, in which case stopping the countdown on any interaction with the dialog would help. In practice, however, people don't seem to have trouble with it so we decided not to add the additional complexity (and risk of bugs).