With a countdown displaying on your products you create something like a scarcity mentality in people. It can create a feeling of fear, anxiety and maybe desperation just because they see that the price will rise in a specific period. It also make someone think that s/he has got only one shot right now. Buying a product then relieves much of the pressure (and the feeling of fear).
The Product Countdown WordPress Plugin is the most powerful scarcity plugin ever created for WooCommerce. With just a few clicks you can create scarcity-based countdown-timers when a WooCommerce product is on sale.