Custom index, stategy to publish items under a certain path

Question

We have this custom index that only contains pages for one section of the content tree. We want it setup so that publishing items under this path reindexes those items automatically. This seems like it should be default behavior but it is not working - we publish the items and no reindex happens. We can tell because old content is still shown on the site for these items, and the correct content is shown after rebuilding the entire custom index.

Our configuration is currently as follows:

<index id="redacted_centers" type="Sitecore.ContentSearch.LuceneProvider.LuceneIndex, Sitecore.ContentSearch.LuceneProvider" patch:source="Sitecore.ContentSearch.Lucene.Index.Web.config">
<param desc="name">$(id)</param>
<param desc="folder">$(id)</param>
<!--
 This initializes index property store. Id has to be set to the index id 
-->
<param ref="contentSearch/indexConfigurations/databasePropertyStore" desc="propertyStore" param1="$(id)"/>
<configuration ref="contentSearch/indexConfigurations/defaultLuceneIndexConfiguration"/>
<strategies hint="list:AddStrategy">
<!--
 NOTE: order of these is controls the execution order 
-->
<strategy ref="contentSearch/indexConfigurations/indexUpdateStrategies/onPublishEndAsync"/>
</strategies>
<commitPolicyExecutor type="Sitecore.ContentSearch.CommitPolicyExecutor, Sitecore.ContentSearch">
<policies hint="list:AddCommitPolicy">
<policy type="Sitecore.ContentSearch.ModificationCountCommitPolicy, Sitecore.ContentSearch">
<Limit>300</Limit>
</policy>
</policies>
</commitPolicyExecutor>
<locations hint="list:AddCrawler">
<crawler type="Sitecore.ContentSearch.SitecoreItemCrawler, Sitecore.ContentSearch">
<Database>web</Database>
<Root>/sitecore/content/centers</Root>
</crawler>
</locations>
<enableItemLanguageFallback>false</enableItemLanguageFallback>
<enableFieldLanguageFallback>false</enableFieldLanguageFallback>
</index>

What configuration would be needed to make items get reindexed when they are published?