Nonskimmer
Captain
Many of the US escort ships are nuclear too. Not all, but many of them. This doesn't include the supply ships, but they and any rotating escorts can certainly keep the primary units (carriers) on station almost indefinitely if required. Even crew change outs aren't unheard of.
Even if the carrier is conventionally powered, supply ships rotate all the time.
Even if the carrier is conventionally powered, supply ships rotate all the time.