Looking at the logs, the last couple of time The Sims 3 has crashed, it quit immediately after Time Machine ejected the remote Time Capsule volume. And it quit immediately, without any spinning pinwheel or crash report. I was running a cracked version of The Sims 3 previously, and didn't have this problem, which suggests that the code that checks for the presence of the Sims 3 DVD is being overzealous and deciding that it needs to quit the game when any volume is ejected.
I will turn Time Machine off and see if this lets me play for any serious period of time.