If 1 member has an open file on his/her computer and another member opens the same file on his/her computer then sometimes files get deleted.
And I finally read this line and I somehow overlooked it. What you want, I don't think you can have. I don't know if it's at all possible to edit one graphic file on more than one computer at a time unless using solution #2 listed below. There are databases which allows more than one user to edit a database file but they are designed to allow this to happen. I would also question if in the past the graphic editing was saved without any edited data loss.
Look at it this way and if I'm wrong, someone will most certainly reply to correct me:
1. User 1 opens the graphic file "Toads.tiff" for editing and starts to edit the left upper corner of the image.
2. User 2 opens the graphic file "Toads.tiff" for editing and starts to edit the lower right corner of the image.
3. After some editing User 1 saves the edits. This writes over the file on the NAS, now this is the new file.
4. For User 2, the graphic image only displays the original image and the editing they have done. Now they save the image. The NAS now has a graphic image that resembles "only" the version of the file that User 2 saved. Any changes User 1 made are gone.
Why does a file get deleted? I can't say but having two users editing the same file does not sound good unless the software was written to support it.
The solution:
1. Do not let your users edit the same file at the same time.
2. Use Collaborative Cloud Editing for Photoshop which requires a Creative Cloud subscription.
Maybe there is a similar way to do collaborative editing without the cloud, but this is going to be a Photoshop feature.