I think the only proven method to be able to consistently stay at the same spot on the search engine would be to continuously build hq links from hq sites to your site, and also build a brand out of your domain, and once the search engine recognizes your brand and your authority in the respective field, your website will be able to consistently stay at that spot thereafter.
I also noticed that some site uses ultra high quality links from new sites that cost a couple of thousand of dollars for the review - these links are really power links, and when combined with an exact match anchor text, that link can put your website as the authority for that term.