If an ArcGIS Server service contains special characters, such as the angle brackets and hyphen (< - >) in the description, the service fails to update any property after publishing from ArcGIS Server Manager.
Stop the ArcGIS Server Service on each machine involved in the site.
Delete the folder for each problematic service here: [drive letter]:\arcgisserver\config-store\services (if these services are in a folder, double-click on the folder and users see the respective services).
Delete the folders for the service here: [drive letter]:\arcgisserver\directories\arcgissystem\arcgisinput (same steps as step 2).
Republish the service from ArcMap without the special characters in the description.