The appleDeveloperTeamID field ("Automatic Signing Team ID") in the Player Settings (ProjectSettings.asset) is not saved unless the Inspector is placed in Debug mode and back to Normal. After that, it is possible to change the value in Normal mode and it will get saved every time until User enters to Play mode or restart Unity, where it will fail to save in Normal mode

To reproduce:

1. Download attached project "appleDeveloperTeamID not saved.zip" and open in Unity
2. Open "Scene" scene
3. Open Player Settings
4. Select the iOS tab
5. Change the "Automatic Signing Team ID" value to something like "abcd"
6. Save project
7. Open ProjectSettings.asset in the Text Editor and search for the "appleDeveloperTeamID" which is empty
8. Change the Inspector to Debug mode using the top right dropdown, and then back to Normal
9. Confirm that "Automatic Signing Team ID" is now empty
10. Change it to "abcd" again
11. Save project
12. Open ProjectSettings.asset in the Text Editor and search for the "appleDeveloperTeamID" which is now "abcd". You can keep changing it and saving and it will change in the file.
13. Enter Play mode and exit Play mode or restart Unity
14. Try to change "abcd" to something else like "1234".
15. Save project
16. Open ProjectSettings.asset in the Text Editor and search for the "appleDeveloperTeamID" which is still "abcd" and didn't register the change once again
17. Changing to Debug mode and back to Normal will fix this again

Notes:
- This issue appears on both Windows and macOS

Reproduced on Unity 2017.4.13f1, 2018.1.9f2 and 2018.2.12f1
Not reproduced on Unity 2018.3.0b5 and 2019.1.0a4