The regulations are a bit vague on this. I don't see anything that requires the immediate shutdown of a translator if the primary is off. 74.1231(e) requires a translator to take steps to avoid relaying the
wrong primary - if off-air pickup was used, this would be most easily complied with by shutting down the translator if the incoming signal got too weak -- though as a DXer I've seen some evidence that many translators simply ignored this regulation.
74.1263(b) prohibits a translator from operating "...during extended periods..." when the primary is off. Of course, "extended periods" is pretty vague. However, it is also noted that a translator relaying an AM daytime-only station may operate at night, while the AM primary is off, only if the AM primary has operated in the previous 24 hours. (so if this non-lawyer was forced to provide a definition for "extended periods", I'd say that means more than 24 hours)
I think someday an AM station
is going to challenge this, leaving the translator on while the AM is off for an extended period, either on purpose to save $$ or due to a difficult-to-repair breakdown. How (and if) the FCC responds will make a big difference in the population of the AM band...
FCC regulation 74.1231(e):
(e) An FM translator shall not deliberately retransmit the signals of any station other than the station it is authorized to retransmit. Precautions shall be taken to avoid unintentional retransmission of such other signals.
74.1231(h):
(h) An FM translator station that rebroadcasts a Class D AM radio broadcast station as its primary station may originate programming during the hours the primary station is not operating, subject to the provisions of Sec. 74.1263(b) of this part.
74.1263(b):
(b) An FM booster or FM translator station rebroadcasting the signal of an AM or FM primary station shall not be permitted to radiate during extended periods when signals of the primary station are not being retransmitted. Notwithstanding the foregoing, FM translators rebroadcasting Class D AM stations may continue to operate during nighttime hours only if the AM station has operated within the last 24 hours.