Clayton's post is correct. You need to add a receive connection on load. Check to see if a record with the date has already been added and if so, maybe disable the submit button and conditionally display some red guidance text telling them that they have already submitted (use conditional formatting to display that).
However, this won't work if your form doesn't close on submit. If users keep the form open, please add a rule that disables submit after they submit once. To do that, add a field to your form to track submits (main data source, or for extra credit you can add as a secondary data source).
Even so, users may still be upset because they may mistakenly submit before they meant to. I recommend warning them in both cases and just saying "You already submitted once today. The next time you submit, e-mail will be sent to the support alias. Please enter your justification here: ..." and provide a text box. That allows the user to submit again if they have second thoughts and the second submit should e-mail some distribution list with the justification. Then, you can refer to that if there is an issue. This way, you reduce your support costs.
:)