The switch or membrane under the “E” key has slight oxidation, debris, or mechanical wear. When the laptop is off or cold, the contact might not close cleanly, but after a few presses or as the laptop warms up, it reconnects properly.
To diagnose a keyboard problem, it's essential to test with the onscreen keyboard or a different keyboard via USB or Bluetooth. If the alternative keyboard works, it's certain that the issue is hardware-related.