We have LPG gas for the stove/oven only (I think) and we have to turn a little button on a gas line that comes in through a window before we can turn on the burners. My question is, should we turn that off whenever we are not using the stove or do we need to leave it open all the time?

Should not matter, as long as you have a detector around the stove to catch a gas leak.

We had city gas and had the same type of button and everytime we were done with the stove we turned it off "just because".

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CH-47 SI

They must find it difficult...

Those who have taken authority as the truth, rather than truth as the authority. --Gerald Massey

My GF turns it off all the time...I leave it on. I bet the house will burn down just so she can say, "I told you so."

Most Koreans turn it off, but I never touched mine and the building is still there! It does not save you any money to turn it off and if the gas line catches fire you will have bigger problems anyway!

some gas lines are metal, some are flexible rubber or plastic tubing. (The type illegal in the US.) They can rupture with age or abrasion or increased pressure.
Some have shut off valves near the stove, some are in the utility area, or at the wall. On most stoves is EASY to leave a burner on UNLIT, or accidentally turn the oven on and it may fail to light. Gas can accumulate. Even as you sleep!

The consequences of igniting an oven or a room with a certain amount of gas inside needs no elaboration!

Turning off the valve does NOT take a lot of effort. It can prevent potential problems, especially with children or smokers in the house. Can you afford the consequences? TURN IT OFF!

PS-most apartments have smoke detectors, required by the US Government Housing Inspectors. Smoke detectors detect smoke and products of ignition, not gas! (Gas detectors are expensive.)

I've been turning it off, because gas make me nervous anyway. We have the rubber tubing kind, and there is what I'm assuming is a little gas detector nearby. All the writing on it is in Korean except for the letters "LPG" on it.

good for you, Violet! Sounds like you do have a detector. The question is- does it work; And even if you learn how to test it, and it does work, it is only useful if you are at home and hear it!