Add geometry attributes tool in ArcMap successfully runs but no fields are added to attribute table

I get this type of error often -- it is very frustrating. Sometimes the tool works Ok if background processing is turned off in Geoprocessing Options, but other times it does not, with one message in the Geoprocessing results saying

TypeError: cannot add field: 'POLY_AREA'.

I have tried, with background processing turned off :

1. run Create Feature Class tool to create a polygon shapefile in British National Grid with M and Z disabled.

2. run Check Geometry tool on blank shapefile, giving "cannot find spatial index" for OBJECTID, FEATURE_ID -1.

3. edit new shapefile to add two polygons

4. run Add Geometry Attributes, perimeter in metres, area in hectares -- SUCCEEDED!
5. delete POLY_AREA and PERIMETER fields
6. turn off background processing
7. run Add Geometry Attributes -- claims to have succeeded, but no fields are added to attribute table
8. turn off background processing again and re-run Add Geometry Attributes tool. Failed to execute, with TypeError: cannot add field: 'POLY_AREA' (whether or not with coordinate system specified.
9. run Add Geometry Attributes tool requesting only perimeter. Failed to execute, with TypeError: cannot add field: 'PERIMETER'

I hope this helps someone make sense of what is going on 'behind the scenes'.

This was solved. The tool ran fine, but the fields weren't displaying in the attribute table. I had to quit out and restart the application. However, this didn't work at first; I had to wait a day and try opening the application again for the fields to appear. If you're encountering this issue and quitting/restarting doesn't work, it may work after some time has passed, or restarting your computer entirely.