That typically happens with me if I have my set-up wrong...primarily if I have the monitor up too high. I have to look up, causing my head to lean back and the back of my neck can only deal with that for a few hours...then I feel like I broke something. Even a slight, very very slight, look up will hurt after a while, make sure you have the monitor at eye-level.
Your joystick base should be level or slightly above the arm-rest of your chair. As with rudder pedals, I would suggest not having your feet on them all the time, unless your actively using them don't keep your feet at that angle, causes all kinds of weird pains. Sitting up straight can help, as long as you don't have bad eyes like me, then it causes eye pains (I have to lean in to see anything even on a 32" TV). Another thing to try is get the most comfy pillow you can find and sit on that, the cushioning on a desk chair wears out fast and that ends up hurting the back/bum pretty back...I have almost worn mine out in 2 months.
And as Waystin said, get up and move, that helps a lot. I do it more often then that because I need constant liquid (dry throat in the winter), but that along with having set up right will help a lot.
Aside from that, it could just be old age.
