I'm a new user, like many who'll read the the vanitygen FAQ and it's not exactly clear why you don't need to resume vanitygen. Does it automatically save its progress to some file?
Password recovery tools like those from ElcomSoft have resuming as a salient feature.
I guess you don't need to save the progress anywhere, because vanitygen is simply generating huge numbers of random addresses and hope to find one that matches your pattern. It's simply a matter of probabilities, you can start/stop the search multiple times, and even run it on multiple computers and stop it when a matching address is found (kinda like "mining", you basically mine random things and expect to find a hash that matches the difficulty).