My survey responses are all accumulating in one email thread.

All of the responses to my survey are attached in one email chain. How do I make sure they come in separately? 

This depends on the email client / webmail that you use, but in general each allows you to break threads and show all emails as a single email instead.

Alternatively, you could change your forms title so that it shows a unique entry, like users full name, or submission ID, etc (depending what serves you best).

For example:

New Submission has been made by Ben D.

a new email would have different ending so it should not become the same thread, like:

New Submission has been made by GrandTrunk

Hope that this helps.

The following guide will assist you in the steps on changing the email subject: How to place form title in the Subject Line of form notification?