I know that the PS3 version comes with Dead Space Extraction with it, but what's the availability for it? First run (like Need for Speed: Hot Pursuit)? Always (like Medal of Honor)? Has EA said anything about it?

Checked all of my usual UK online retailers as well as some Europe based sites. They all list the PS3 version as limited edition however it is the only Playstation 3 version on sale. I would assume it is the same elsewhere, but obviously best to check. It is also likely that it will NOT be 'limited' and that it will continue to be on sale after the games launch.  
 
EDIT: I remember reading that the edition with Extraction would stay on sale and that they plan to release it in download form on PSN at some point. However I cannot remember whether that was purely speculation or whether that was an official statement from EA...I will try to locate the link for you.

Until it runs out? I was able to find a limited edition of Hot Pursuit at Target on black friday last year. 

I don't think it should be that hard to find.  I'm ordered mine a couple months ago but you should still be able to order it anywhere you go.

Ironically for me, it's the regular edition that was apparently running a little thin. Amazon sent me an email saying that they unfortunately had no regular copies, weeks into my preorder, left and instead have changed my order to the limited edition for no price alteration. 
 
Maybe EA is surprised to not find the limited edition being preordered off the virtual shelves as fast as they expected, but in any case they seem to adamant to get em outta there.

I should maybe clarify. I'm asking more of how long after launch it'll be available. I know the copies at first will be Limited Edition, but I'm wondering how long afterwards.

So my understanding is that all pre-orders will be Limited Edition right?
 
I've had my copy pre-ordered from Amazon for about 2 weeks, there's an ongoing thread in the Amazon forums over whether or not the Amazon "standard" edition is the Limited Edition, since all they list is standard and Collector's.
 
If I don't get Extraction, I may put it in a box and return it since that was the only reason I pre-ordered, as I am still grinding through Dead Space 1 at this point.

I don't know. but the biggest franchise 'COD black ops' was never sold out. never. even lots of people have bought it so far. I can still find special edition at retail stores along with Halo CE version. so DS2 will be the same.