This article is from the X-Men Comic Books FAQ, by Kate the Short (email@example.com) with numerous contributions by others.
The Savage Land is one of the fixations of Stan Lee, co-creator of much
of the Marvel Universe, that has survived longer than other favored plot
ideas of his (how many Marvel comics are taking place around a circus
currently, for instance?).
The Savage Land is a direct tribute/descendant/ripoff of those classic
"Lands that Time Forgot" sf/fantasy stories. It's in that "peninsula"
sticking out of Antarctica, and the horribly complicated history of it
can be found in various editions of the OHOTMU. Basically, it was set up
as a type of alien wildlife preserve, and it's been run by a variety of
administrations since (currently, no one is in charge of the elemental
machineries that keep the Savage Land warm and tropical in the midst of
the vast ice field).
The X-Men have had numerous adventures in the Savage Land, and are good
friends with Ka-Zar, the main hero of the Savage Land, as well as with
the tribe of the Fall People. In none of those cases have the X-Men ever
lost their powers just from being in the Savage Land, although various
villains they've fought there have dampened their powers while in there.
This question largely comes from X-Men: the Animated Series fans, since
the Savage Land in X:TAS apparently drains the mutant powers from those
mutants who visit it. (It may be that the X:TAS Sinister had something
to do with that as well.) This is most certainly not the case for the
comic-book X-Men and Savage Land, though.