component.html

// Parent component which repeats a list style component (growth-units)
// If I observe "this.qualificationsList" I can see it updating when I add to it
// These updates do not seem to be passed down into "qual.units" for each repeated instance

<dom-module name="growth-template">
    <template>
      <template is="dom-repeat" items="[[ qualificationsList ]]" as="qual">
          <growth-units
              units="[[ qual.units ]]">
          </growth-units>
      </template>
    </template>
    <script>
        Polymer({
            is: "growth-template",
            properties: {
                qualificationsList: {
                  type: Array,
                  value: []
                }
            }
        });
    </script>
</dom-module>

// Child-Repeated list-style component with a repeater inside
// After intitial load, "this.units" loads the correct data.
// Although everytime the source for "this.units" is updated, it is not reflected in this component.
<dom-module name="growth-units">
    <template is="dom-repeat" items="{{ _toArray(units) }}" as="unit">
      <a>
          <span>{{ unit.value.name }}</span>
          <small>{{ unit.value.code }}</small>
      </a>
    </template>
    <script>
        Polymer({
            is: "growth-units",
            properties: {
                units: {
                    type: Object,
                    value: {}
                }
            },
            _toArray: function(obj) {
                return Object.keys(obj).map(function(key) {
                    return {
                        name: key,
                        value: obj[key]
                    };
                });
            },
        });
    </script>
</dom-module>

yo i don't think you can do that, the outside template is created only once and the internal templates then, can be updated...
i don't remember exactly where i have read that but that is i believe how it works, try something like...

 <template>
   <template is="dom-repeat" items="{{ _toArray(units) }}" as="unit">
      <a>
          <span>{{ unit.value.name }}</span>
          <small>{{ unit.value.code }}</small>
      </a>
    </template>
</template>