Hello, this bug appears to still exist in 2.8.3. The bug is not limited to the Append tool in Model Builder. It appears in the Spatial Join and Merge tools and presumably in any tool with a Field Map input parameter. It is not possible to save or persist field mappings within a Field Map parameter as the tool(s) will dynamically refresh the field mappings whenever the tool is run or opened/edited.
An example scenario: I want to use Spatial Join to join field 'X' from Layer B to Layer A. I configure the field mappings to output only field 'X' and save the model. I run the model and the Spatial Join performs successfully but outputs all fields from both Layer B and Layer A - ignoring my field mappings to output only field X.