First off, sorry that you're running into ranking problems. It's never fun, but always turns into a learning process.
Upon inspection, it seems as though your link profile is lacking a set of links with integrity. Those that come from natural evolution of the lifespan of a linkworthy site. Looking at your link profile, sorting by external links to the root domain shows top links are from directories in large part. Granted, they are directory links with good authority, I would surmise that there are a lot of competitor links you could obtain as well as the ever-sought-after editorial-type links.
You're right. Big brands have these and they will continue to grow in SERP saturation within your vertical. The best thing you can do is be dynamic, target time-sensitive news items, provide better content and build your network of bloggers, social authorities, youtube users and grow your footrpint the right way.
Look to the link profiles my friend.