While there are a few alternate options, end of the day you may be at the whim of this finick-y Google Webmaster Tool, and Google’s valuation of your landing pages.
For example: In general, sitelinks are a positive for both established brands and searchers.
It’s easier for consumers to find what they might be looking for, and it’s easier for a brand to serve up these pages without a need for navigation.
However if you happen to be Nike, dominance of a SERP using sitelinks on your own ecommerce site is particularly handy, as of course Nike products can be purchased from many different retailers.
You have very little control over how these appear.
That said, if you’ve demoted a Sitelink and just can’t get it to go away, it’s time to evaluate why you want that sitelink out of the picture in the first place.