Most people don't realize the power of personal connection on the job.
I have many clients today that have lost their jobs and are looking for new employment. Unfortunately, they have worked at their respective companies for a very long time and they find themselves unable to get 
back that one specific position.
Even though I do coach them to 'reach for the stars', there is a law of diminishing returns. After a certain amount of time (let's say 4-6 months), one needs to be realistic about their search. If you are busting your butt getting interviews and not getting that position, it may be time to click your search down a notch and focus on easier pickings. This happens frequently with C-Level clients that NEED to have another C-Level position. Honestly — they're not many C-Level (or others of that ilk) spots out in business-land today.
My suggestion — instead of beating your head against a wall — take a lower position that will be easier to attract/lock-in. When you get into the invite-only party, show them you're able to do much more than you've been hired to do. Most likely, they will see your capabilities over time and offer you increased responsibility or a better position (with increased pay).
But this scenario only comes with a successful and clear set of personal connections in the new job (I will talk about building personal connections later this week). And you will only get those if you are On The Job.
So don't be so picky and go get that position. Good things sometimes don't come to those who wait.