Form missing submissions or submissions deleted?

We are missing several submissions to a form we use to collect interest/applications for a program we do weekly. I downloaded the Excel spreadsheet on March 20th and so I have all of the entries from before march 20th but the most recent submissions on the form are from the 27th of march, so essentially, I'm missing from the website all of the entries from before March 27th, but more importantly the week between March 20th and March 27th we have none of our entries either in our downloaded excel or in the website submissions... Any ideas? Do you have perhaps any records of this we cannot see or access?

I have reviewed your form and I can see what you're reporting, the last submission seems to be from March 27, 2018. Upon checking your account activity logs it seems like some submissions were deleted, you may check this as well following this guide: https://www.jotform.com/help/370-How-to-View-Your-Account-Activity-Logs 

You may also share us the document so we can check the missing submissions on our end. Please send it to support@jotform.com using this thread id on the subject "1440669". 

We will wait for your response. 

I found it in the activity. Is there any way we can recover these lost submissions? I'm sure it was an accident.

Unfortunately, once a submission is deleted, it can not be recovered. What you can do to back up your data in the future, is to integrate with Google Spreadsheet: https://www.jotform.com/help/228-How-to-Integrate-Form-with-Google-Spreadsheet 

I've tried that with some forms, but unless i'm mistaken, the second you make a change to even the wording or position of a question, it makes the integration not work anymore. Is there a workaround for this?

Editing of the spreadsheet that is integrated with the form can break the integration and we do not recommend it. Also, editing of the form, such as adding a new field or editing of the field labels will break the integration. 

You can always, re-integrate your form with the Google Spreadsheet when the integration stop working. 

How to Integrate Form with Google Spreadsheet

As an alternative, you to create another sheet and import the data to a new sheet from the sheet that is integrated with your form. This can be achieved with the import range function - http://www.makeuseof.com/tag/how-to-import-data-from-other-google-spreadsheets/ 

This will allow you to edit the second Sheet without breaking the integration. 

Regarding your deleted submissions - You can try to find the data you deleted inside of the emails that were sent to you when the form was submitted. You can check the email logs on your account:

How to View All Your Form Email History