About a week and a half ago, we spotted the new raid lockout extension feature on the patch 3.2 PTR. It's not until this morning that Blizzard (specifically Eyonix and Vaneras) officially announced that the feature was coming, along with some clarified details.
The details are mostly what we expected: Extending your lockout will let it roll over into the next lockout period, consuming your instance ID for that day (in the case of heroics) or week (in the case of raids). You can extend your lockout more than once, probably indefinitely, but Eyonix wasn't specific on how many times you can do it in a row. I assume indefinitely. The extension is also on a per-person basis, meaning if you PUG someone into your 25man run, they can't screw you by extending their lockout. That also means it's not a raid leader decision. At least, not mechanically. It's up to the individual to click that extension button.