Leave email in inbox when responded to

Who is your email provider?

That is definitely not a function of the mail client on the Mac unless you created a rule to do that.

There is no setting. That isn't a feature. Possibly a bug.

The entire conversation should be viewable in Sent (with Organize by conversation set), but it doesn't move things out of the Inbox.

I don't know why you are seeing disappear from the inbox and see the whole conversation if that is turned off.

What is the email service provider? Gmail doesn't work with Mail since it is not really an IMAP account.

… not go hunting around for something that was received Monday in Thursday's sent folder just because I responded to it on Thursday.

You have sent folders for each day? That seems incredibly difficult to manage. Maybe that has something to do with it.

I have never seen that in any mac... reply should not move the message out of the inbox.

It seems that you may want to turn off "organize by conversation", but regardless it should never do what you describe.