If anyone doesn't want to use mods, or has enough already, the burglar can just be reset with the command console. As soon as he or she appears on the lot, you can see the name, and resetsim works just fine. The burglar doesn't get deleted, just sent back to the purgatory where NPCs hibernate whenever the game doesn't need them. (I also do this with cops that try to catch my teens out after curfew.)
In big families, I never seem to get burglars no matter how long I play. I wondered why for a long time, but then I realized that they only come when everyone's asleep. So if I have a sim with a late work shift (chef, musician, athlete, etc.) who stays up most of the night, the burglar can't show up. Even babies who are awake in their crib seem to prevent a robbery, and since they only sleep a few hours at a time, their sleep schedules rarely synch with the rest of the household. I guess they make better witnesses in TS3 than in real life.