How to reproduce:
1. Open the attached project
2. Select "Controls" Input Action Asset from the Assets folder
3. Duplicate it by pressing Ctrl+D
4. Select the new "Controls 1" Input Action Asset and click "Edit asset" in the Inspector window
5. Add a new Action to the "New action map"
6. Collapse the "First" Action
7. Place it between the "First" and the "Second" Actions
8. Click Save Asset

Expected result: Action IDs remain attached to their names, as seen in the Inspector window
Actual result: Action IDs remain attached to their positions in the list and not their names, as seen in the Inspector window

Reproducible with package versions: 0.2.10 (2019.3.8f1), 0.9.6 (2020.1.0b3), 1.0.0-preview.6 (2020.2.0a5)
Could not test with package versions: 0.1.2 (2019.3.8f1, project errors)

Notes:
-This doesn't reproduce if the Input Action Asset is saved after the 5th step, this is shown in the attached results table
-It is impossible to drag an Action under another Action if the top one isn't minimized.
-The duplication of the Asset isn't mandatory for reproduction but it helps to compare Action IDs