Exporting data like history

Hi. How do we design a form that keeps a running  history of the interaction we're having with each client ( separately? )

If I understood you correctly you want to have all data that are coming from your clients stored like history.

When someone submits you form all data that are entered inside of your form will be saved on your JotForm account. Inside of this article you can find out how to view your submissions: 

http://www.jotform.com/help/269-How-to-view-Submissions 

You can also download submissions or data of your form into Excel, CSV and PDF format. For excel, you can follow this guide:

http://www.jotform.com/help/44-How-to-Export-Form-Data-to-Excel 

When you export your data you can separate them for each user.

You can also integrate your form with Google Spreadsheet, Dropbox or Google Drive and save you data there as well.

If I did not understood your question correctly please explain in more details what you want to achieve.

Hope this will help. Let us know if you need further assistance.