Jump Solving stops jumping weirdly, something recognizable?

I simulated a JumpProblem, and I simulate it many times (100) using the ensemble functionality. Very rarely (like 1 time out of 100) the solution suddenly stops changing, see this plot of example:
(the green line)

There’s a lot of jumps going on, like towards 100,000 maybe (I sample every 1 timestep to reduce the size).

Everything is kinda weird, and I am trying to figure out what is happening, figured I should check if someone has any ideas. Could there be something like maxiter that gets hits (however, no warnings are generated)?