School Mac Lab deleting files automatically from Downloads & Desktop

This is happening consistently on certain (most) computers in our 30 device graphic design computer lab: over night anything downloaded or saved to the desktop is deleted and does not show up in the trash folder (although the trash folders aren't empty). The students are high schoolers so I know not every reported issue is real (there is so much human error here) but the downloads folders on all of the affected devices have old files from around the same date and earlier but nothing from the last 2 school years which leads me to believe it is some sort of automated system. I asked the school IT manager and he claims no such program is being run on these devices and won't look into it. He is sure it is the kids deleting things. I inherited this lab mid-year from a woman who was by all accounts a bit unstable. She quit suddenly with strange reasoning so I have no contact with her whatsoever. How do I figure this out so I can fix it?

Just so you know, I am somewhat tech savvy but only in the layman's way. Code is beyond what I can do unattended/without super detailed instructions but I have used some in the past. To say that I have written code would be too strong a word - I grew up in the MySpace era and the early internet days, so I've copied chunks of code. I am old enough to have learned how to use simple functions of MS-DOS as a child and have successfully used Terminal and similar utilities with detailed directions. Even after several google searches, I have no idea where to start with this issue.