N.H. Rev. Stat. Ann. § 4:24

The governor, with the advice of the council, may respite from time to time, for stated periods, the execution of a sentence of death upon a convict while proceedings are pending that may result in a new trial, or if they regard further time necessary for a proper investigation and consideration of facts bearing upon a question of absolute or conditional pardon pending before them, or if it appears to their satisfaction that the convict has become insane, or, being a female, is quick with child, until they have had sufficient time and opportunity for such investigation and consideration or the cause is removed.