The question has false premises, because the New York Times article is misleading. The Antarctic Treaty itself does not expire. You can read the text (PDF) of the treaty; there is no provision for expiration. What there is is a provision saying that thirty years after the treaty enters into force, any consultative party (i.e. any party that does serious Antarctic research) can call for a review of the treaty, at which amendments can be formally proposed more easily than normal (by majorities, not unanimity). If the consultative parties to the treaty haven't all ratified the amendment within 2 years, any party can withdraw (this is the only time a consultative party can withdraw). Note that this isn't the same as "the treaty expires" -- in fact, reviews to the Antarctic Treaty have been possible since 1991, and none have been called.
The only treaty where 2048 is significant is the Protocol on Environmental Protection; 2048 is the year when that treaty becomes open for review, under slightly different terms than the Antarctic Treaty. Again, this is not expiration; it carries the possibility of the treaty dissolving no less than 3 years after the review, and only if an amendment is adopted at the review and not ratified by enough consultative parties. This is an environmental treaty; the provisions where no nation can make new claims in the Antarctic and no military activity is allowed there are under the actual Antarctic Treaty, which is already up for review (and hasn't had one called in the 24 years it's been eligible).
The Outer Space Treaty is more like the Antarctic Treaty, not its Protocol. Like both of them, it does not expire. Unlike either of them, it allows any party to withdraw with one year notice, and always has (whereas a consultative party to the Antarctic Treaty or its protocols could only withdraw after a review session).