Teacher needs help! My students' Illustrator files vanishing, get "the file does not exist" message

Hello! I have a huge problem that I need help with. I teach graphic arts at the high school level and I have had 5 students in the last few days have their illustrator files vanish. I see them every other day and they are assigned a local user account. Other students use the same computers, but they all log out at the end of the period. My students have been working on a big vector portrait project for the last 3 weeks, and they have been trained to log in, open illustrator, open their .ai file, then save it in their local user folder. 

What's weird is, all of the sudden some of them have randomly lost their files. When we go to click on "open recent files", we can see the file name (see photo - "jj.ai"), but when we click on it, we get the message in the other photo ""file does not exist": jj.ai"

We have tried everything to locate it. I've spent a ton of time trying to figure it out myself, and have had our district IT helping and we are perplexed. The missing files are random and I am always in the room when other students are in here, so I know there isn't any foul play. 

The most interesting thing is, the rest of their files are still there. They've done multiple projects and they are still there, but at random, these files are just vanishing. 

I've had to tell a few kids now they've lost all of their work. Praise the Lord they've handled it well, but we've all been there where you lose something you've invested a ton of time in and lose it so it's just difficult to tell them it's gone. 

I've searched online for answers and haven't found anything. I've tried all of the following:

-restrarting, relogging in

-searching the computer for the file name

-watching youtube videos for help

-going to the data recovery folder (the loss wasn't from a crash)

Thank you in advance for any advice!!! God Bless!!!