Broken datasource every time the mxd reopened

[SantoshV]

I have authored a Map MDX from shapefiles, every time I reopen few of the shapefile data source is broken, I use the Repair data source option to fix it, but then again when I open the mxd the data source of the same few shapefiles are broken, what am I missing here?

Also, note that when I publish this it the ArcGIS Server after file packaging I get an error 

Where the service publishing fails.

I am using ArcMap 10.6.1

[MichaelVolz]

I would suggest creating a file geodatabase and importing the shapefiles into the file geodatabase as feature classes.  I would then register the folder location of the file geodatabases with ArcGIS Server (AGS), so the data is not copied to the AGS server.