I am able to edit multiple items in the View Metadata ->Edit Metadata dialog in ENVI 5.3. After you make your edits and select 'Ok' in the Set Raster Metadata dialog, the header will be updated so it is normal behavior to close the file and then reopen it in the Data Manager.
Are you making all updates before closing the Edit Metadata dialog which saves the changes?

Typically if the header information is not retained, it is because
1) the file you are trying to add/edit metadata is not an ENVI format .dat but some other format such as HDF or DIMAP or other external format. These formats have custom readers and may not consider the ENVI .hdr.

Or 2) the directory or file is not read/write capable and needs permissions. It may be that the .hdr is written to another directory.

Can you confirm if either of these may be the case?

Neither case 1 or case 2 is happening. We do some manipulations to raster data in IDL, then import it into ENVI and save it as a .dat file. After we have save the file, the metadata dialog box is opened and the other steps are performed. I will have to check again tomorrow, but what I remember is that the dialog box disappears before the the 'OK' is clicked. It disappears when we add the 'data ignore value' option. We were used to the image disappearing and then being redisplayed with the updated metadata - but now it doesn't reload.