Answer: It will lose revenue.
Explanation: Elasticity of demand basically measures the degree of responsiveness of the quantity demanded to a slight change in the price of the commodity/service. Imagine holding an elastic band on one hand and tugging at it with other hand. It will respond to your pull (by stretching), but the length to which it can stretch is it's elasticity. It might be significant or it might be very unnoticeable.
Hence if the demand for movie rentals is described as "highly elastic" it simply means the consumers' response to a slight change in price (either increase or decrease) would be significant. Therefore if a video store raises the price of a rental under the given circumstances, it will lose revenue for sure.
This follows the law of demand that states clearly, "...all things being equal, the higher the price of a commodity/service,the lower the quantity demanded for that commodity/service and, the lower the price of a commodity/service the higher the quantity demanded for that commodity/service." This is a certainty as far as the commodity is classified as a normal good.