Dear Jess,
Welcome to the forum here.
Generally, if you use the formula reference to update the cell, the cell should be updated.
To confirm whether the issue is related to the specific file, I'd like you to copy the part of cells and the reference cells to a newly created file and then do a test to see if it works in your environment.
Meanwhile, to confirm how you update the cell, I'd like you to upload some screenshots showing the sample data source and how you update the cell for our reference.
Note: Remove any private information before uploading the screenshots.
Moreover, if the file contains no features not supported in Excel for web, I suggest you upload the file to a online place such as OneDrive for Business or SharePoint Online and do a test in Excel for the web to see if the issue disappears in Excel for the web.
Thanks for your effort and time.
Cliff