Q:

Energy of black hole

If a black hole attracts and engulfs light, then why doesn't the energy of the black hole increase to form a star once again? Black holes form when a star burns off its energy and collapses, so it should make sense that, since the photons engulfed in the black hole have some energy, that the black hole should reform into a stellar entity.

A:

You're confusing yourself. A black hole state has nothing to do with the lack of energy in a system. A star doesn't become a black hole because it can't fuse stuff anymore (i.e. the end of its energy), it becomes one because of what happens to the star after its fusion process ends**. Black holes form when a high amount of energy is concentrated at one point*, and this happens in massive stars because of the gravitational collapse of the star onto itself, when its radiation pressure (from the outward force due to nuclear fusion) goes out of balance with its gravitational force. It doesn't have anything to do with how much energy is added to or present in the system. When a black hole engulfs light or energy in general, it just becomes a slightly larger black hole, and it cannot turn back into a star as you mention. 
Edit: I thought I should add in explanations for some of the things I've said.
*A system with mass energy $M$ (i.e a star of mass $M$) becomes a black hole when the spherical region it is contained in has a radius of $$\frac{2GM}{c^2}$$
($G$ is the gravitational constant, $c$ is the speed of light in vacuum.) 
**Stars start out by fusing light elements like Hydrogen, and this happens faster in more massive stars. This fusion process usually abruptly stops at Iron, because the energy needed to fuse it is greater than the energy released, in simple terms. The flux of energy outward exponentially reduces, gravity takes control, and the star collapses. Depending on the mass of the star, this can lead to it becoming a neutron star or a black hole.

