Non-profit organizations are required to comply with all normal information return reporting requirements. This means they need to collect and remit employment taxes as well as file Forms W-2, etc. Additionally, non-profit organizations are also required to file form 1099-MISC whenever in the course of its activities it pays more then $600 during the year to a non-corporate entity or natural person.
Accordingly, if the total of the payments during the course of the year exceeded $600, then the organization needs to issue the 1099-MISC. Your organization should also file 1099-MISC for every year they have not as well.
Potential penalties are approximately $50 for every 1099 not issued that should have been.
Because it is impossible for me to identify and consider ALL the relevant facts, this advice is not intended or written to be used for the purpose of avoiding penalties, and cannot be used for that purpose.