Sitelinks tend to rely on Google being able to identify a pattern in your internal linking structure. If you do not have a clear internal link structure Google will have a harder time determining what (if any) sitelinks you should have.
I am not sure what minimum traffic level Google requires for sitelinks to appear (if any). I know many sites with thousands of uniques per month that do not have sitelinks. I also run a small specialty site that only has 200 uniques per month and it does have sitelinks. This small site has been featured in national news and enjoys high link popularity which is probably why it has sitelinks.