I'm not sure I understand what the problem is here...the curve interpolation is relative to the frame the particle enters the event....so if it enters again and again, it will loop again and again. This is by design.
When the particle enters the event for the second time, according to the logic, it should only rise and fall three times and then stop rising and falling. But now it has not stopped, and it is constantly rising and falling.
The value of "duration" in the "spread" operator should refer to how many frames to complete the animation of the curve, right.
So I think when the particle enters the event for the second time, "30" frame should stop the undulating behavior.
But you have a Time Test that sends them out every 30 frames, then the Object Test in the next event sends them back. So those particles are cycling in and out of that event every 30 frames, over and over, forever. If they stayed in the event longer than 30 frames, you would see that the interpolation would stop. You can test this by setting the Time Test operator condition to 60 instead of 30. They will stop at 30 frames until they go back out and then back into the event after 60 frames.
