There are two reasons firms strive to maintain stable (sticky) prices, the first is that these companies know that consumers do not take to kindly to price fluctuations, consumers tend to prefer stable and predictable prices that do not fluctuate rapidly with changes in demand, so there is pressure on them to keep prices stable and not upset consumers. Also, these companies are afraid of cutting their prices for fear of 'price war' i.e. rivals/competing firms might simply match the price cut.