So it's funny that I've found this years later, due to the question I had to answer if Eidolon's need sleep on the Material Plane.
The reason this came around is that I came up with a similar house rule after having made a mistake in the very first session with my players as a new GM.
The house rule was this.
When the summoner is asleep, whether it be natural, from battle, or a spell, that his Eidolon would persist on the Material Plane. The drawback is that she (the Eidolon) would gain 50% concealment on both AC and Attacks. Meaning that she was halfway between her Home Plane and the Material Plane.
It gave an interesting perspective early game because it did indeed help with her tanking abilities early on in the game. As the Eidolon took on more evolutions (the ones that gave it 50% concealment all the time), the unconscious status is more prominently a hindrance.
This actually ended up developing some character specific plot points (as in this world, Summoner's typically have to resummon their Eidolons), which I'm still working with today. Thought I'd add my two cents on the subject though!