Under documents, check in the electronics art folder and then the sims 3. You may have to have enabled seeing hidden files to see it, but there is a folder for the saves. After a patch earlier, all saves transformed from a normal file to its own sub-folder in that "saves" folder. If you save that (the whole folder marked with the same name as the save game in question) somewhere else (maybe the desktop), it should work.
After you've re-installed the game, you just put the save file back in the corresponding folder. I've never re-installed my game in this fashion before, but I've played around with these files a lot to fix my save errors and I'm pretty confident the whole save file is in those folders. Someone else can maybe verify this 100%.