This hasn't happened to me, but it would be pretty crappy to find out you lost your domain because the script that your domain registrant uses to renew your domain name is slower than park.io's script.
Once your domain has expired, it will be in Auto-Renew Grace Period (for 0-45 days), followed by a 30-day Redemption Grace Period. At the end of the Redemption Grace Period, you will not be able to renew your domain name. Your domain name will be released for registration by third parties.
https://www.icann.org/resources/pages/expired-2013-05-03-en
For example, daily.sh will be available on their platform on 2016-09-30, but it actually expired back in 2016-07-01.