Oil price elasticity - different for up/down?

Just another random thought.

Price elasticity is very different for many items depending on the time frame. For example, for durable goods, we are very price sensitive in the short term - buy less and use what we have if the price increases all the sudden. We keep using the 5 year old fridges, stoves, we don't go out to get new dress shoes every other week unless it breaks, we wait for few months before replacing that crown on molar teeth that cracked... but eventually, we have to purchase a new toilet, get a new car, replace that wig.... you get the point. Same argument applies to oil as well.

But, is it different for when the price goes up/down? Let's consider this from empirical point of view.

UP, Short Short Term: People don't buy as much if price suddenly skyrockets.
UP, Short Term: People realize that price hike isn't temporary and starts filling up again. Behaviours are hard to change. They aren't going to suddenly start eating at the soup kitchen, but they realize that it's a battle between two dark liquids. Bottle of Coke vs gallon of oil.
UP, Long Term: They change their behaviours after realizing that it's impossible to drive when lacking the chemically-made-fume-generating liquid . Coke wins.
Price sensitivity changes direction twice. Very sensitive, to not sensitive to sensitive.

DOWN, Short Short Term: OMG oil's down, let's fill up my tanks.
DOWN, Short Term: OMG it's actually low. Let's unfasten my belt and start buying oil.
DOWN, Long Term: Where is the incentive to change my habit back?
Price sensitivity doesn't change direction.

I might have gotten some stages wrong, or have faulty logic running somewhere. But my point is, price going up and down is not the same thing. Going up is introduction of limitation. Going down is demolition of the limitation. So, it ALWAYS matters which direction the demand/supply moves to.

No idea what triggered this whole debacle here....