In the Táin Bó Cúailnge, the men of Ulster are disabled by a curse placed upon them by Macha to feel her labor pains in their hour of greatest need, thus disabling them when the army of Connacht attacks.
Cúchulainn is immune to this curse. As I understand it, he is immune because he is yet a beardless youth, and so a curse upon the men does not apply to him. This makes sense, since, when an exhausted Cúchulainn sleeps three days, the boys of Ulster come to the defense.
I've also read that the explanation of his immunity is due to his demi-godhood, being that he is the son of Lugh, the Long Arm.
Related question: Why isn't Súaltam disabled by Macha's curse?