The caption of an enumeration is always editable in the modeler. The value, displayed as the name column in the edit enumeration dialog, is not editable. If you are unable to modify the caption value (first column in the enum edit dialog) then file a ticket with Mendix support.
Changing the value of the enumeration in the java class will not work as the proxy class is generated from the model. So changing the enum value in the class will not lead to a change noticed by the modeler and will be overridden once you deploy your application. If you really need to change the value for your enum, add the new value a fix the errors after deleting the value you wanted to change (for example visibility on forms and logic in microflows).
When you change the java code make sure that you save it in Eclipse and do a commit on the teamserver. You can double check if the java code was changed when you redeploy locally. Check Eclipse afterwards if the changes are still there.