Ordinarily, as the pressure in the reservoir drops, the flow decreases, to the point that at some point the well has to be pumped (oil no longer reaches the surface on its own).
The oil industry is one of constant innovation and design, and the time needed to drill a well has been cut to 1/4 what it was just 30 years ago, not to mention that we have the ability to drill (and steer as we go) directionally and horizontally as well.
Here’s a couple of articles that are interesting.
The first (from 2006) talks about the difficulties and new technology in the exploration business. Also has some references to the geology of the area that think that the entire 5 miles down to the oil is a bunch of Mississippi mud.
The second article (from 2009) is about the deep water Thunder Horse site that is in production.
What amazes me is that with all the money, time, cost, technology, risk, etc. on these projects, it is left up to the company man to say “Do it. That’s what the pinchers (BOP) are for!” (I know, I’m repeating myself!)