Do pilot lights stay lite on gas fireplaces when turned off?

depends on the fireplace. If it's a woodburning fireplace with a gas flame to start it, the gas to the fireplace is totally turned off when you turn the key (and remove it to a kid safe place, I hope), so you must use a match/grill lighter to relight when the gas is turned back on. If it's a ceramic log fireplace, not designed to burn wood, it may have a pilot (which you can turn off for summer, inside the lower heat exchanger grill, looks just like a gas waterheater control set, and works just like it, too). It may be one of the newer ones, which uses a sparker to light, and doesn't have a pilot. Best way to find out is to look inside on a dark night. If you see a yellow/blue flame in there, it's a pilot.