Can't print participant's image in name badge
Image URLs were the subject of a security release in CiviCRM 5.10.3.  My guess is that you've uncovered a bug related to this, especially if they printed in the past.

My recommendation would be to take your test site (I hope you have one!) and revert it to CiviCRM 5.10.2 to see if it resolves the issue.  If so, I would use the test site to print the badges, and report the bug on https://lab.civicrm.org, referencing this Stack Exchange question.