Obviously, with the international space station you need to do some station keeping when you're falling into the atmosphere. However, I saw the following image showing the Halo orbit that the Deep Space Climate Observatory is in:

It seems like once it hits its stable halo orbit, that the speed is between 0.15km/s and 0.05km/s. At what point would there be a red flag? Is there an easily calculable escape velocity for an orbit around a Lagrangian? What would scientists be looking for to alert them that they need to do corrections for such an orbit?

Obviously, with the international space station you need to do some station keeping when you're falling into the atmosphere. However, I saw the following image showing the Halo orbit that the Deep Space Climate Observatory is in:

It seems like once it hits its stable exponentially unstable halo orbit, that the speed is between 0.15km/s and 0.05km/s. At what point would there be a red flag? Is there an easily calculable escape velocity for an orbit around a Lagrangian? What would scientists be looking for to alert them that they need to do corrections for such an orbit?