Best advice I can give you is talk to your sensei. Since he's presumably been doing this for a while, he should be able to give you better advice than we can. It might be that your stiffness has less to do with how much you are training and more with how you train-- you might be holding your muscles tensely, for instance, in a way that makes them more likely to stiffen up afterwards. As an experienced instructor who can watch you train, your sensei can pinpoint these problems and help you adjust them. He can also evaluate your overall physical condition and calculate the specific effect the training regime that he teaches will have on it.
No matter how experienced someone on this board might be, we can't see your condition or watch you move, and we don't know what the particular classes that you train in are like. We're just guessing, but your sensei should know.
David Sims
"Cuius testiculos habes, habeas cardia et cerebellum." - Terry Pratchet
My opinion is, in all likelihood, worth exactly what you are paying for it.