Well, in theory, if conditions don't change, an orbit remains unchanged forever.

However, in practice, in our Solar system for example, you've got planets orbiting the Sun, each at their own pace, and every planet is exerting some gravitational force on other planets as they pass each other by, making tiny changes in their orbits.

So, orbits do change over HUGE periods of time (but we're talking slight changes over millions of years), but they don't really decay.