This is tough because of the human aspect. You can implement the perfect reporting system and have a great culture, but you may continue to have the occasional straggler. I think this gets harder the larger an organization is.

It sounds like you are on the right track with the repeated communications. It may be helpful to speak with the employees who reported late. Have a confidential discussion with them to determine the root cause of the late reporting. Was is computer access? Fear of retaliation? General naivety? Does the form have a confusing user interface? Is it stored somewhere deep in the intranet? There are lots of possibilities.

Like everyone else is saying it just takes time making sure the employees trust management enough to report without repercussions. We just let go 2 managers who both made employees afraid to report anything because they would scream at them. I just try to emphasize and repeat it in any trainings all the employees get. When we do investigations I try to make the employees involvement very positive with no discipline, that will come after if necessary. I send out toolbox talks occasionally that outline how exactly to report an incident and the process we go into for investigations to show we actually care and want to find a root cause. If you can find a way to get employees involved with the investigation process, that might help

This can be difficult to do if employees are fearful that they will get in trouble, feel if they report an incident, and get in trouble. Thus this should be a learning opportunity to improve on the situation. Is there a different process of doing this task or other training that may be needed? It also is important for the Safety person to develop a relationship with the employee to learn what the employee needs to complete their tasks safely and efficiently. Also, the buy-in from frontline supervision and managers is a plus to ensure reporting done.