Exact steps for others to reproduce the error
Switch to "UV and mesh selection sync mode", then choose "Face" select - image disappears. If apply "Mask" modifier, image stays in place.
The way to make it work without bothernig "Mask" modifier:
- Click RMB between islands
- Switch to "Sync" mode and then "Face select" (now image should disappear)
- Disable "Sync" mode and re-select image
- Go back to "Sync" mode and click RMB between islands
After saving it seems to be OK.