I’ve been simulating some halo orbits and also running into stability issues

It seems it’s pretty typical and depends on the integration method used, as well as the timestep

In general it is quite a hard problem to solve. Mathematically, it’s a very difficult problem. But also computationally, it is almost impossible to fully simulate an n-body system without getting chaotic orbits. Then you have to either cheat (by manually tweaking trajectories) or just picking a pretty small time range for the simulation