A laser's energy is supplied from an outside source, e.g. through optical, electrical or chemical pumping of the gain medium. So the gain medium is not being borne away by its conversion to light energy, if that's what you mean! The energy comes from a separate power supply. However, depending on exactly how you mean your question to be read, one could say that the medium is borne away and must be replenished in an Atom Laser which outputs a coherent beam of atoms from a Bose-Einstein condensate.
Coming back to "light" lasers: you are in principle right: the gain medium atoms / molecules cycle repeatedly exactly back to their beginning states in outputting the laser light and can do so indefinitely. However, at a practical level, no gain medium is immortal. This is especially so for dye lasers: all fluorophores eventually bleach, which means that they have a very specific "mean number of cycles before failure" and thus an exponentially distributed useful lifetime. The transition eventually destroys the fluorophore. It can be very slow (e.g. in an erbium doped fibre amplifier), but it is inevitable. Solid state gain mediums are also eventually degraded by lasing - particularly in high power systems such as Q-switched lasers. Gas lasers leak their gas slowly: I have heard a saying that one should switch an unused HeNe laser on the shelf every six months to help forestall such leaking, but I do not understand how this can help and think that it is probably an experimentalist's urban myth.