Use the adverb indefinitely to describe something that happens for an unlimited amount of time or to an unlimited extent. Kittens could bat around a ball of string indefinitely.
When your cousin postpones her wedding indefinitely after her fiancé’s “business trip” to Las Vegas, you probably want to hold off on buying a gift. They may work things out, but sometimes people intend indefinitely to be synonymous with forever. Like, “We can’t keep fighting over that weekend I spent in Las Vegas indefinitely…”