I there a way to recover form submissions when the account was maxed out?

I there a way to recover form submissions when the account was maxed out?  We had to last minute change our newsletter and contact forms on our site to Jotform before a tradeshow.  Our account reached its submission limit over the course of the show and I'm sure we lost newsletter sign ups and contact submissions.  What happens on the side of the user submitting the form in that case?  Is there any way to recover submissions from that time?

You may enable the auto-fill feature in your form, so those who can not submit your form, can try later: https://www.jotform.com/help/227-How-to-Enable-Auto-Fill-on-Forms