Have you heard about link velocity misha?
If you Google "Michael Jackson," you'll see sites about the artist. However, when he died a sometime ago, you would have seen almost entirely sites dedicated to News Updates and the Death. The reason for this is that these sites got a ton of links at once, and shot to the top of the rankings. After that initial link burst, they received fewer links and now I'd assume they're receiving none. When they lost that link pressure, they slowly left the top rankings because Google no longer saw them as relevant.
By gradually building up the number of links being built to your site, and keeping those links growing over several months; you'll show Google that your site is meant to stick around for the long term. In my opinion you should never stop doing SEO on your site. You can lessen the pressure once you reach the top, but it's best to keep some links coming in so your stay there and widen the gap between you and your competitor.
Summing it all up, start slow with your link building and make sure you're in it for the long haul. And keep things White Hat. Blasting links at a site using Black Hat techniques is only asking for short term rankings and a potential banning of your site.