Stiff as in you are losing flexibility, or are your joints stiff? I've only been studying since last fall, but very intensely (5-6 hours/week plus seminars and extra-curricular work).
Yes, you will loosen up in time. The more quality stretching you do, the faster that will be. Some people are really tight to start out with, giving them much farther to go. I started out pretty flexible because I've been in martial arts for a long time before starting aikido (restarting, actually - I studied a few months in another dojo a number of years ago).
With stretching, if you want to really make progress you have to hold your stretch for more than 30 seconds, probably three sets or so. This can make stretching routines take time, but if you do them you will notice actual progress. Usually, pre-class stretching is just to loosen you up and does little for actual flexibility improvement.