I had this annoying issue where Android Studio kept deleting my top-level project file (.iml) whenever I do a gradle sync. For months I had no idea why and Google search doesn’t seem to show this as a common issue. Finally today I got to the bottom of this.
The issue was the casing of the file names. For the project file, I had mixed capital and lowercase, whereas the project folder name was all lowercase. This inconsistency was due to a move of the project from a windows environment to a mac where I had a different folder name.
The fix for this issue was simple: Close the project in Android Studio and delete all the .iml files. Then use File > Import project and select the project folder and this will regenerate all the .iml files. The new .iml files should now match the case of the folder.