Are there any instances where short run demand/supply is more elastic than long run cases? Conventionally both demand and supply for goods and services are both more elastic in the long run than in the short run.
My Question

Is there ever an instance where demand and/or supply for a given good be more elastic in the short run than in the long run?

That being said if there is never such an instance, does there exist a general proof refuting such an instance?
It is possible.  We normally think demand and supply are more elastic in the long run because consumers/firms have more options in the long run.  For example if gas becomes more expensive consumers can buy more more fuel efficient cars.  

So what if consumers or firms are more constrained in the long run?  This could be the case when goods are storable.  

Suppose I need to drink coffee every day or I get a headache.  At home I have a canister of coffee that I use every day.  If coffee doubles in price I can hold off buying and hope the price comes down, so I am fairly elastic.  In the longer term though I'll run out of coffee and I'll need to buy more regardless of the price.  

Of course in the even longer term maybe I can stop my caffeine addiction so I become more elastic again.  

This maybe isn't the best example, but the key thing to think about is how constrained the agent is at each point in time.  When people are more constrained in their options they are less elastic.