Redshifted Photon Energy

Consider the following scenario: I am on a train moving away from you. I throw a ball to you. The speed of the ball as measured by you when you catch it, is less than the speed of the ball as measured by me when I threw it. Where did the energy go?

This situation is precisely the same as the Doppler shift situation you describe. In both cases, there's no problem with energy conservation, because the energies in question are measured in two different reference frames. Energy conservation says that, in any given reference frame, the amount of energy doesn't change. It says nothing about how the energy in one frame is related to the energy in another frame.

If it is a gravitational redshift, to a first, non-rigorous order, the energy loss is due to the fact that it is moving in a gravitational field, and thus is gaining potential energy while losing kinetic energy.

If it is a redshift due to the actual motion of the object, then the energy lost in the redshift is imparted to the object doing the emitting since energy and momentum are conserved in the emission process--it is an energy transfer due to recoil.

Redshift is due to expansion of the universe. Not just the space, but space time. So it's not just the space between the source and the observer which is stretched. The light itself is also stretched. This means a ten minute burst of light will be stretched to a 11 minute burst of light. (Just an example). The extra minute of light means a reduction in intensity, like stretching a piece of putty makes it thinner. The total energy remains constant but spaced over a longer period.