There seems to be a lot of conflicting terminology when it comes to the anti-magic field and the eidolon. I have thoroughly gone through eidolon and anti-magic field to see what I can come up with seeing as I can't find an official post anywhere. I only see one instance that states that it will dismiss an eidolon.
Summoned creatures of any type wink out if they enter an antimagic field. They reappear in the same spot once the field goes away. Time spent winked out counts normally against the duration of the conjuration that is maintaining the creature. If you cast antimagic field in an area occupied by a summoned creature that has spell resistance, you must make a caster level check (1d20 + caster level) against the creature's spell resistance to make it wink out. (The effects of instantaneous conjurations are not affected by an antimagic field because the conjuration itself is no longer in effect, only its result.)
And this line most people seem to think overrides the entire rest of the description of the spell. the very first line is.
An invisible barrier surrounds you and moves with you. The space within this barrier is impervious to most magical effects, including spells, spell-like abilities, and supernatural abilities. Likewise, it prevents the functioning of any magic items or spells within its confines.
While an eidolon does count as a summon it is not labled with SP, SU, nor is it a spell.
It also states that it does not affect conjurations with an instantaneous duration. If you wanted to treat summoning an eidolon as a spell or spell like ability and format the power out into a spell format. it would either have a duration of
Permanent
The energy remains as long as the effect does. This means the spell is vulnerable to dispel magic.
Or instantaneous
The spell energy comes and goes the instant the spell is cast, though the consequences might be long-lasting.
The eidolon cannot be sent back to its home plane by means of dispel magic, but spells such as dismissal and banishment work normally.
Since it is not subject to dispel magic that would mean the duration is instantaneous. and thus not subject to antimagic field.
In addition, due to its tie to its summoner, an eidolon can touch and attack creatures warded by protection from evil and similar effects that prevent contact with summoned creatures.
I would also rule that this would be a similar effect that would prevent contact with summoned creature since it does exactly that.
I have also seen people post that if a summoner enters an antimagic field it ends his life link ability and sends the eidolon whisking back to its home plane. if that were the case here is the first line of the spell unfetter. This spell breaks the life link between you and your eidolon. That would be a pretty dumb spell if it just sent your eidolon home.
My personal opinion is that unless there has been an official faq post it would not affect an eidolon. sorry for the long post but eidolon vs antimagic shell full of contradicting wording.