Particle Emitter Breaks in emission. Help?

The reason for this gap is that particle systems have a maximum number of particles that can be rendered at any one time.

The reason for the limit, is that each particle system is rendered with a single mesh, and Unity has a built-in upper limit for the number of vertices that any single mesh can use - 65536. Each particle uses 4 vertices, so that works out as 16384 particles (although in a test I just did, the total wouldn't go higher than 16250 particles... I guess there's something else going on there which causes the slight discrepency).

To solve your problem, turn the emission levels back down enough so that the "gap" stops occurring, and then if you need a denser effect, add a duplicate particle system in the same place.

You might even want to make a prefab of the original system, and then add instances of the prefab until it's dense enough - this will mean you can adjust the parameters in the prefab to affect every instance in your scene in one go.