Particle System fails to emit() after last particle dies

Version of Unity: 5.3.1f1/p1

I have a particle system that needs to emit bursts of particles on irregular periods, so I was doing this though script. This works fine while the period is less than the particle lifetime since the last emit (meaning there are still active particles), but if this period is greater than that, the system does not emit and does not throw an error.

I verified this is the case with a simple scene that just contains a single particle emitter (I used the default) with the startLifetime set to 1.0 and emission turned off, then I added the following script component:

 using UnityEngine;
 using System.Collections;
 
 public class TestingPSDelay : MonoBehaviour {
 
     private ParticleSystem ps;
 
     private float dt = 0.0f;
     private float ed = 0.5f;
     // Use this for initialization
     void Start () {
         ps = GetComponent<ParticleSystem> ();
     }
     
     // Update is called once per frame
     void Update () {
         dt += Time.deltaTime;
         if (dt >= ed) {
             dt -= ed;
             ed += 0.1f;
             ps.Emit (1);
             Debug.Log ( "Next ed = " + ed );
         }
     }
 }
 

The console output is as expected with "ed" slowly growing, but after "ed" > 1.0, the system no longer emits particles even though the console output continues.

Pretty sure this is a bug.