Sharepoint links reverting to "Saved as" files on local drive

We have a team of 4 that are working on several Excel files in sharepoint. We have come across some issues with regards to the linking of documents.

It seems that sometimes 2 or more users will be in the file linking fields and as soon as the person saves and closes, it somehow doesn't feed through any information or incorrect information. As soon as you open the files again it seems to populate again and then retains the info when closed.

We also have instances where if we save these files to our local desktop, it updated the links in Sharepoint which now links to the desktop version of the file. 

We need to be able to be in the files all together and be able to save as we go and have those changes stay for all users. Have we missed a step when we created these files in Sharepoint? Autosave is on, on all users.

Regards

Tania