Your workout data measured by Zones is saved to Apple Health on Apple Watch.
Apple Watch synchronize iPhone for healthcare data.(not Zones app)
Please check the following in order to determine where the cause is.
Zones need health permission to measure your workouts.
Check the Permissions of Apple Health.
If it is the same error even if you save again, please try restarting Apple Watch device.
(If there is an unsaved workout, a save dialog is displayed when starting zones watch app.)
Workout of less than 30 seconds will not be recorded.
If the exercise time is less than 30 seconds are not recorded.
Please exercising for more than 30 seconds.
if "SAVED" is displayed and app switch to the top screen, your workout data was saved to Apple health successfully.
Make sure iPhone's Apple Health has a workout data.
Synchronization of dealth data between Apple Watch and iPhone may not be normal.
Please try the following.
Please enable iPhone and Apple Watch to communicate.
Apple Support: If your Apple Watch isn‘t connected or paired with your iPhone
Synchronization of healthcare may take time. Please wait for a while and check again.
Synchronization may resume by rebooting.
If there is a problem with Apple Health's sync, these data will not be updated either.
A bug may have been fixed with the latest iOS, watchOS.
If it can not be solved by the above,
Unpair and repair as "New Apple Watch" will recover in many cases, but please note that the data during that time will be lost.
Apple Support: Set up your Apple Watch