I would look closer at the ignition switch. It sounds like your power is getting cut out. When you first turn on the ignition switch you also get a beep when it initially powers on. If the power cuts out and back on again, you will get the beep again...
That is a strange one, electrical gremlins are never fun. Does this happen when the engine is hot or cold? If only hot, it might be something related to an intermittent electrical component starting to fail. How often does it happen? I assume it is n...