You are using Email to Case Premium and are unaware why a particular field was updated after a new email from a customer was added to a Case.
Out of the box, Email to Case Premium only performs field updates to particular fields.
For example, when a case is created, Email to Case Premium has the ability to set the following fields:
If you notice that a field such as Case Status is being updated when a customer responds to a Case and are unsure why, the update is likely being performed by a local Workflow, Process Builder process, or an Apex Trigger.
Traditionally, administrators could usually track down where the update is occurring by reviewing the full list of Field Updates in Setup or reviewing all of the Process Builder processes / Apex Triggers on the object being touched.
Starting in Winter 19, Salesforce has released a pilot feature called "Where is This Used?", which allows administrators to easily see what local automation is interacting with a specific field. This ultimately makes it much easier to track down the automation performing the field update that you may not be aware of.
So for example, if you're not aware of why Case Status is being updated, you could simply navigate to the Object Manager | Case | Fields & Relationships | Status. From there, you would click the "Where is This Used?" button and see a full list of all the local automation interacting with the Case Status field.
At this time, the "Where is This Used?" feature is in Pilot. To enable for your Org, please open a case with Salesforce Support.