Internal references are disappearing?

tl;dr - excel is deleting reference formulas and leaving behind whatever the value was that was last input into that cell before it deleted the reference. Why is it deleting the reference and how do I stop it?

Background info:

My company uses an excel spreadsheet for calculating material costs when bidding for jobs. There are 12 different sheets in the workbook that have totals at the bottom from various vendors, and then a 13th sheet that displays and adds the totals of each page for a grand total. These are all in the same workbook. I've provided a mock-up attached of the problem area's visual set-up.

How it's set up:

Each 0.00 is a reference to the cell on each tab that totals the whole page. The reference looks something like ='Tab 1'!E104 and then a simply sum in the subtotal, multiplied for tax below that, and then the grand total being a sum of the two cells above it.

The issue:

It seems that sometimes while the file is being moved around (all within linked DropBox folders), the cells that hold the individual tab references all lose their references and are just replaced with whatever value was in the cell at the time it disconnects. I've tried recreating this issue without luck (only one employee is experiencing it, but then I have to redo all of the references on the file when it happens). He'll move it from one DB folder to another, add whatever data he needs to, and then move it back to a primary DB folder. At some point in that transition, all references are lost. There are no #REF (or any other kind of) errors - for example, the reference would have pulled $150 over, but now when you click on the cell, you don't see the formula I stated above, just that number as if it had been typed in rather than pulled from a reference cell.

I've spent all day trying to figure this out for him so that it stops happening - I made test files and moved them around all over the place from Desktop to different DB folders and back. I had a theory that it was a Trust Center issue but have adjusted those settings on his system to trust the folders he works within and it still happened. I also tried thinks that I knew would probably break a file and would hit Enable Content thinking maybe when he got that prompt that was what was doing it but the references in my test files stayed even after all of this stress testing.

Does anyone have any insight as to what's going on and how I can stop it from happening anymore? Thank for you making it to the end if you got this far, and even bigger thanks if you can provide any insight!