Tokamaks can also be operated in steady-state, at least theoretically. The reason a tokamak is pulsed is due to the fact the toroidal current is driven inductively, so there is a limit to how long you can keep increasing the current in the central solenoid. However there are other methods, for example, neutral beam injection and electron cyclotron current drive. You can even exploit the bootstrap current (self-generated by collisional processes in the plasma) to obtain a near 100% non-inductive toroidal plasma (this is called "advanced tokamak" regime).
Anyway, the older generation of devices was pulsed for engineering reasons (like non-superconducting coils getting too hot). The current generation of device is solving most of these and is limited by MHD instabilities alone (neoclassical tearing modes, mostly), if we can get active control mechanism working, then will be finally approach the long-pulse or steady-state regime.