De acordo com as regras:
Eidolons are treated as summoned creatures, except that they are not sent back to their home plane until reduced to a number of negative hit points equal to or greater than their Constitution score.
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The eidolon remains until dismissed by the summoner (a standard action). If the eidolon is sent back to its home plane due to death, it cannot be summoned again until the following day.
De acordo com as regras de convocação (ênfase minha) ...
Summoning: a summoning spell instantly brings a creature or object to a place you designate. When the spell ends or is dispelled, a summoned creature is instantly sent back to where it came from, but a summoned object is not sent back unless the spell description specifically indicates this. A summoned creature also goes away if it is killed or if its hit points drop to 0 or lower, but it is not really dead. It takes 24 hours for the creature to reform, during which time it can't be summoned again.
Como a criatura invocada está sendo reformada no plano atual, eu diria que quando um eidolon é petrificado, ele pode ser descartado e retomado (incorrendo na penalidade normal de um minuto para conjurar o ritual para invocá-lo).
Eu me lembro de algumas explicações melhores de como criaturas convocadas funcionam, mas não consigo encontrá-las no momento.