Can I have my responses saved or emailed to me for each reply?

Unsure of definitions, so where “reply” is a collection of entries on a form from a user, and “response” is the administrator’s communication back to that user: Can I do one or both of two things.  One; can I store my (administrator) “response” to a user, so that it is compiled together with the record of that user’s form “reply”.  Two; can I have my “response” emailed to my email address, as well as to the user?

Setup a notifications to be sent to your email address: https://www.jotform.com/help/25-Setting-Up-Email-Notifications 

If you also want to send an email to the person who fills and submits the form, then setup an autoresponder: https://www.jotform.com/help/26-Setting-Up-an-Autoresponder-Email 

Those guides are not updated yet for JotForm V4, if you are on V4 already, simply click on Settings, then on Emails:

Let us know if you need more help.

I don't see a means for achieving my task.  I do have notifications set to send emails to me, but these only respond to user submissions.  I do not get an email when I send a response to the user.

Could you explain what you mean by "I do not get an email when I send a response to the user."?

From where are you sending a response to the user? Do you mean that when you receive the notification, and click on the reply button, you wish to also send that reply to yourself? 

Yes. That is it.  You have it.  I want to keep track of my conversations.  Retaining the full threads would be ideal, especially if I could record them in the same file with the user's submission.  But if that is not possible, at least to have that communication sent back to me would be helpful.  Presently, I copy my reply (which I enter into your email reply form), before sending it, and paste it into a different document, so that I can keep track of what I said to whom.   This is not very efficient.

Your reply should be saved in the "Sent Mail" folder of your email provider. But if you still need to forward your reply to yourself, simply Cc to yourself, example:

Let us know if you have more questions.

Yes.  This is the thing.  I believe I used to get my responses back into my Sent box, but I have been inactive until lately, and I don't find that now.  I don't know why that changed, but it doesn't go into my Sent box now.  Why?  Any ideas?

 I believe I used to get my responses back into my Sent box, but I have been inactive until lately, and I don't find that now.  I don't know why that changed, but it doesn't go into my Sent box now.  Why?

You must be referring to your email service provider. Can you tell us what was the email client you were using?

Normally, email service will always put the Sent messages in the Sent mailbox. This is the normal configuration/setup most email service i.e Gmail, Outlook, yahoo mail.. and so on.

This configuration is not related to the form emails though. 

Please provide more clarity on the issue and we will investigate more.

Thanks.

My email server is Comcast xfinity.  Can you see my settings for my form?  I believe I have them set properly for this.  As far as my configurations for my email server, I don't know what I would do differently.  I have a Sent mailbox, and it is filled with other emails that I sent, just not those initiated from within Jotform.  What can you suggest?

Everything appears to be well setup, I would suggest you to contact your email provider, or try a different email provider.