So I figured this out myself. My EventHub had a Cleanup policy of "Compact" and not "Delete". Apparently there is a requirement when pushing messages to an EventHub with "Compact" cleanup policy to have a PartitionKey included, which I was not including. The only way I found this out was the LogAnalytics table named AZMSDiagnosticErrorLogs. It had a single error repeated:

compacted event hub does not allow null message key.

There were no error messages anywhere else that I could find.

So to fix, in my Stream Analytics output settings, I included a column for the Partition key column.