You’re using too many particles. You seem to have reached the limit of how many particles can show on your screen (IIRC 16k is the limit).
When there are over 16k particles in the area, particles will appear/reappear based on your camera’s position, choosing to render the ones that are the closest to you, and not rendering those farther away. It’s always trying to choose which particles should be part of those 16k and which shouldn’t.
To fix this, use less particles. You’ll surely have to make the exchange from many/small particles to fewer/bigger particles.