Steps to reproduce:
1. Open attached project "getkey.zip"
2. Open "GetKey bug" scene
3. Run the project
4. Hold "A" and "S" keys down
5. Notice how after a new scene loads Unity Editor indicates (Input.GetKey(KeyCode.S) && Input.GetKey(KeyCode.A)) as false even though keys are still being pressed (gif attached)

Note: Editor successfully detects input after scene change if one key is being pressed. Editor detects multiple keys IF they are pressed at the exact same moment (happens rarely, you have to be very quick).

Reproduced with: 5.3.0f4, 5.3.5f1, 5.4.0b21