Generally yes, woods tend to lose their springiness over time, however this depends on the kind of wood you buy, a good quality club will last a long time and take a fair amount of abuse before it starts to decline, a cheaper club (like a dunlop/john letters you would find at sportsworld as part of a cheap set) would not last as long.
depending on how often you played you can get a good 5 years out of a driver/wood, obviously if you play a lot and use a cheaper set you are likely to lose performance after a couple of years. In any case the face of the wood will start to show tiny cracks when its on the way out, this is before it loses its springiness